# Schrödinger, Erwin

# SCHRöDINGER, ERWIN

(*b*. Vienna, Austria, 12 August 1887; *d*. Alpbach, Austria, 4 January 1961)

*theoretical physics*.

Schrödinger’s father, Rudolf Schrödinger, inherited an oilcloth factory, which, although run in an old-dashioned manner, was successful enough to free him of financial worries. After studying chemistry he turned to his real interests—painting and, later, botany—and published a series of scientific papers in the *Abhandlungen* and *Verhandlungen der Zoologisch-botanischen Gesellschaft in Wien*. He married the daughter of Alexander Bauer, professor of chemistry at the Technische Hochschule in Vienna; Erwin was their only child.

Schrödinger attended public elementary school only once, for a few weeks in Innsbruck, while his parents were on vacation. In Vienna an elementary school teacher came to his home twice a week to tutor him; but, in Schrödinger’s opinion, his “friend, teacher, and tireless partner in conversation” was his father. In the fall of 1898 Schrödinger entered the highly regarded academic Gymnasium in Vienna. As was then customary, the curriculum emphasized Latin and Greek, the sciences being somewhat neglected. Schrödinger wrote: “I was a good student, regardless of the subject. I liked mathematics and physics, but also the rigorous of the ancient grammers. I hated only memorizing ‘chance’ historical and biographical dates and facts. I liked the German poets, especially the dramatists, but hated the scholastic dissection of their works.”

As a student Schrödinger regularly attended the theater in Vienna and was a passionate admirer of Franz Grillparzer. He kept an album containing programs of the performances he had seen and made extensive annotations on them. He did not, however, neglect his studies. In 1907, during his third semester at the University of Vienna, he began to attend lectures in theoretical physics, which had just been resumed after a nearly two-year interruption following the death of Boltzmann. Friedrich Hasenöhrl’s brilliant inaugural lecture on the work of his predecessor made a powerful impression on Schrödinger.

Schrödinger highly esteemed Hasenöhrl and attended his lectures on theoretical physics five days a week for eight successive semesters. He also was present at the mathematics lectures of Wilhelm Wirtinger and those on experimental physics of Franz Exner, whose laboratory assistant he later became.

In 1910 Schrödinger received the doctorate under Hasenöhrl, and the following year he became assistant to Exner at the university’s Second Physics Institute, where he remained until the outbreak of war. During these years Egon von Schweidler was *Privatdozent* at the university; Schrödinger was obliged to supervise the large physics laboratory courses, a duty for which he was very thankful all his life because it taught him “through direct observation what measuring means.”

Schrödinger served in World War I as an officer in the fortress artillery; and in the isolated areas where he was stationed, he often had time to study physics. In 1916, while at Prosecco, he learned the fundamentals of Einstein’s general theory of relativity, which he at first found quite difficult to understand. Soon, however, he was able to follow Einstein’s train of thought and the relevant calculations; he found much in the initial presentation of the theory that was “unnecessarily complicated.”

As early as 1918 Schrödinger had as sure prospect of obtaining a position; he was to succeed Josef Geitler as extraordinary professor of theoretical physics at the University of Czernowitz (now Chernovtsy, Ukraine). “I intended to lecture there honorably on theoretical physics, at first on the model of the splendid lectures of my beloved teacher, fallen in the war, Fritz Hasenöhrl, an beyond this to study philosophy, deeply immersed as I then was in the writings of Spinoza, Schopenhauer, Mach, Richard Semon, and Richard Avenarius,” The collapse of the Austro-Hungarian monarchy prevented this plan, and after the war he worked again at the Second Physics Institute in Vienna. As a reslult, Schrödinger’s first scientific papers were in the experimental field. In 1913, at the summer home of Egon von Schweidler at Seeham, Schrödinger collaborated with K. W. F. Kohlrausch on a work that was awarded the Haitinger Prize of the Imperial Academy of Sciences and that was published as “Radium-A-Gehalt der Atmosphäre in Seeham 1913.” At Seeham, Schrödinger met Annemarie Bertel, whom he married on 6 April 1920.

Shortly after his marriage Schrödinger moved to Jena, where he was an assistant to Max Wien in the experimetnal physics laboratory. He left Jena after only four months, in order to accept an extraordinary professorship at the Technische Hochschule in Stuttgart. He remained there for only one semester; in the meantime he had received three offers of full professorships-from Kiel, Breslau, and Vienna. He would have preferred to succeed Hasenöhrl at Vienna, but the working conditions for university professors in Austria were then so poor that this alternative was unacecptable. Instead he went to Breslau, where az few weeks after his arrival he received and accepted an offer to assume the chair formerly held by Einstein and Max von Laue at Zurich.

While at Zurich, Schrödinger worked chiefly on problems related to the statistical theory of heat. He wrote papers on gas and reaction kinetics, oscillation problems, and the thermodynamics of lattice vibrations and their contribution to internal energy; in other works he elucidated aspects of mathematical statistics. In an article on the theory of specific heats and in a monograph on statistical thermodynamics he gave a comprehensive account of the latter subject.

Although Schrödinger published several contributions to the old quantum theory, he did not pursue that topic systematically. His first papers on relativity pointed to a second major field of interest. In addition to these works, and his early papers on relativity, Schrödinger made a detailed study, through both measurement and computation, of the metric of color space and the theory of color vision. The main results of his efforts were an article in J. H. J. Möller and C. S. M. Pouillet’s *Lehbuch der Physik* and the acceptance by physiologists of his interpretation of the relationship between the frequency of red-green color blindness and that of the blue-yellow type.

In the meantime, on 25 November 1924, Louis de Broglie defended his dissertation before the examining committee at the Sorbonne: “Recherche sur la théorie des quanta. “The contents of the dissetation first became known through a direct communication from Paul Langevin to Einstein and then, more generally, through publication in the *Annales de physique*. At first no physicist except Einstein—ws willing to believe in the reality of the Broglie waves.

As in his first quantum papers, of 1905, Einstein at the end of 1924 again hypothesized “a farreaching formal relationship between radiation and gas”; but by the latter year he was concerned primarily with the properties of the gas. Basing his analysis on what is today known as Einstein-Bose statistics, he obtained expression for the fluctuation in number of molecules that hinted at interference effects.

Schrödinger, who in 1925 was also investigating problems of quantum statistics, was “suddenly confronted with the importance of de Broglie’s ideas” in reading Einstein’s “Quantentheorie des einatomigen idealen Gases. 2. Abhandlung,” which appeared on 9 February 1925 in *Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin*. He recognized that Einstein had introduced a fundamental new approach, but he sought “to recast it in a more pleasing form, to liberate it from Bose’s statistics,” which he deeply disliked.

Shortly before the middle of December, Schrödinger completed a paper on this topic, “Zur Einsteinschen Gastheorie,” recorded as being received by *Physikalische Zeitschrift* on 15 December 1925. In an important and still unpublished letter to Einstein dated 28 April 1926, Schrödinger gave the following evaluation of his results: “I can ... assert categorically that I have really achieved the liberation I mentioned above... . I stress the determination of the frequency spectrum in ¬ 3. This whole conception falls entirely within the framework of ‘wave mechanics’; it is simply the mechanics of waves applied to the gas instead of to the atom or the oscillator.”

Schrödinger, who generally expressed his judgements in an intensely emotional way, termed the earlier Bohr-Sommerfeld quantum theory unsatisfactory, sometimes even disagreeable. Seeking to apply the new ideas to the problem of atomic structure ,he “took seriously the de Broglie-Einstein wave theory of moving particles, according to which the particles are nothing more than a kind of ‘wave cxrest’ on a background of waves,” As is evident in a letter of 16 November 1925, from Schrödinger to Alfred Landé, Schrödinger conjectures on this topic date from the beginning of November 1925 and therefore from before the conclusion of his paper on Einstein’s gas theory.

The intensity of Schrödinger’s work on the problem increased as he saw that he was on the track of a “new atomic theory,” and it reached a peak during his winter vacation in Arosa. On 27 December 1925 he wrote to Wilhelm Wien, editor of the *Annalen der Physik* in Munich that he was very optimistic: “I believe that I can give a vibrating system ... that yields the hydrogen frequency *levels* as its eigenfrequencies.” The frequencies of the emitted light rays are then obtained, as Schrödinger observed, by establishing the differences of the two eigenfrequencies respectively.

Consequently the way is opened toward a real understanding of Bohr’s frequency calculation—it is really a vibration (or, as the case may be, interference) process, which occurs with the same frequency as the one we observe in the spectroscope.

I hope that I will soon be able to report on this subject in a little more detail and in more comprehensible fashion. In the meantime I must learn more mathematics, in order to fully master the vibration problem—a linear differential equation,similar to Bessel’s, but less well known, and with remarkable boundary conditions that the equation ‘carries within itself’ and that are not externally predetermined.

The letter confirms what is already known from Schrödinger’s publications and from other statements: that, as must have seemed logically consistent from the physics of the problem, he originally developed a relativistic theory. It must be emphasized, therefore, that Schrödinger worked out the relativistic version only at the end of 1925 and not, as historians of science had believed, in the middle of that year. The equation now known as the “Klein-Gordon equation” does yeild the correct nonrelativistic Balmer term, but it gives an incorrect description of the fine structure. Schrödinger was deeply disappointed by this failure and must have thought at first that his whole method was basically wrong. Today it is known that the reason for the failure lay not in this bold initial approach but in application of the theory of relativity,, which, however, has itself been abundantly confirmed. The relativistic Schrödinger equation is obviously correct, but it describes particles without spin, whereas a description of electrons requires the Dirac equation. At the time, however, only the first steps had been taken toward an understanding of electron spin.

After a brief interruption Schrödinger took up his method again, but this time he treated the electron nonrelativistially. It soon became apparent that he had arrived at a theory that correctly represented the behavior of the electron to a very good approximation. The result was the emergence of wave mechanics in January 1926.

Schrödinger published the results of his research in a series of four papers in the *Annalen der Physik* bearing the overall title “Quantisierung als Eigenwertproblem.” The first installment, sent on 26 January and received by Wien the next day, contains the first appearance in the literature of his famous wave equation. written out for the hydrogen atom. The solution of this equation follows, as Schrödinger put it. from the “well-known” method of the separation of variables. The radial dependency gives rise to the differential equation

In fulfilling the boundary conditions one obtains solutions only for certain values of the energy parameters, the stationary values. This seemed to Schrödinger to be the “salient point,” but in Bohr’s original theory—as its creator stressed from the beginning—it was one of the two fundamental postulates that had remained unexplained. Schrödinger emphasized that, in his theory.

the ordinary quantization rule can be replaced by another condition in which the term “integral number” no longer appears. Rather, the integrality occurs in the same natural way as, say, the integrality in the modal numbers of a vibrating string. The new conception can be generalized and, I believe. penetrates very deeply into the true nature of the quantum rules.

In solving the differential equation for the radial function. Schrödinger received expert assistance from Hermann Weyl. A crucial element in their rapid success was the fact that the mathematical theory had already been completely worked out by Richard Courant and David Hilbert in their *Methoden der mathematischen Physik* (1924).

In his second paper (23 February 1926) Schrödinger gave a sort of “dervation’ of his *undulatorischer Mechanik* in which he drew on the almost century-old work of William Rowan Hamilton. Hamiton was aware that geometrical optics was only a special case of wavelengths, and he showed how to make the transition from the characteristic (iconal) equation of geometrical optics to the differential equation of wave optics. Hamilton introduced the methods of geometrical optics into mechanics and obtained an equation similar to the iconal equation and now known as the Hamilton-Jacobi differential equation. In it the index of refraction is replaced, essentially, by the potential energy and mass of the mechanical particle.

In Hamilton’s work Schrödinger thus found an analogy between mechanics and geometrical optics. And, since geometrical optics “is only a gross approximation for light,” he conjectured that the same cause was responsible for the failure of classical mechanics “in the case of very small orbital dimensions and very strong orbital curvature.” Both would be only approximations for small wavelengths. Therefore, he said:

Perhaps this failure is a complete analogy to the failure of geometrical optics, that is, the optics with infinitely small wavelengths; [a failure] that occurs, as is known, as soon as the “obstacles” or “openings” are no longer large relative to the real, finite wavelength. Perhaps our classical mechanics is the

completeanalogue of geometrical optics and. as such, false... . Therefore, we have to seek an “undulatory mechanics”—and the way to it that lies closest at hand is the wave-theoretical elaboration of Hamilton’s model.

Consequently, Schrödiger introduced into his development of wave mechanics conceptions that differed completely from those underlying the quantum mechanics formulated by the Göttingen school. He himself stated; “It is hardly necessary to emphasize how much more agreeable it would be to represent a quantum transition as the passage of energy from one vibrational form into another, rather than to represent it as the jumping of electrons.” In many passages Schrödinger (like Heisenberg) expressed his views in an almost polemical tone: “I ... feel intimidated. not to say repelled, by what seem to me the very difficult methods [of matrix mechanics] and by the lack of clarity.”

Despite his distaste for matrix mechanics, Schrödinger was “convinced of [its] inner connection” with wave mechanics. Hermann Weyl, to whom he had presented his purely mathematical problem, was unable to “provide the connecting link.” Thereupon Schrödinger temporarily put aside his conjectures on the matter; but by the beginning of March 1926, much earlier than he had thought possible, he was able to show the formal, mathematical identity of the two theories.

The starting point for this analysis was the following observation:

Given the extraordinary, it is ... odd that these two new quantum theories agree with each other even where they deviate from the old quantum theory. I note above all the peculiar “half-integrality’ in the case of the oscillator and the rotator. This is truly remarkable, for the starting point, conception. method, and ... entire mathematical apparatus appear to be fundamentally different for each theory.

Schrödinger remarked that Heisenberg’s peculiar computational rules for functions of the 2*n*variables—*q*_{1}, *q*_{2}, ···, *q*_{n}, *p*_{1}, *p*_{2} ···, *p*_{n} space and impulse coordinates—agree exactly with the computational rules that are valid in ordinary analysis for linear differential operators of *n* variables *q*_{1}, ···,*q*_{n}. The correspondence is of such a nature that each *p*_{1} in the function is replaced by the operator α/α_{q1}. As a result Schrödinger rewrote the equation *pq*—*qp* = *h*/2π*i*(first formulated by Bron) simply as because the operator on the left side. applied to an arbitrary function of *q*. reproduces this function. On this basis Schrödinger proceeded to show the complete mathematical equivalence of the two theories. The matrices can be constructed from Schrödinger’s eigenfunctions and vice versa.

With the demonstration of the mathematical identity of wave mechanics and matrix mechanics. physicists at last came into possession of the “new quantum theory” that had been sought for so long. In working with it they could use either of two mathematical tools: matrix computation or the method of setting up and solving a partial differential equation. Schrödinger’s wave equation proved to be easier to handle. Moreover, physicists were more familiar with partial differential equations than with the new matrices. Therefore, Schrödinger’s methods were more widely adopted for the mathematical treatment of the new theory. He contributed substantially to the elaboration of that treatment in his next two papers, especially through the development of his perturbation theory.

In his first publications Schrödinger had spoken of the wave function ψ as something that could be directly visulized—a vibration amplitude in three-dimensional space. He sought to interpret *ψψ̄* as electric charge density and hoped to establish physics on a thoroughgoing wave conception. Since, however, experiments clearly indicated the existence of strongly localized particles, he attempted to introduce the concept of the wave group: “One can try to construct a wave group of relatively small dimensions in all directions. Such a wave group presumably will obey the same laws of motion as an individual image point of the mechanical system.”

Schrödinger attempted to develop this conception in “Der stetige Übergang von der Mikro- Zur Makromechanik.” It soon became apparent, however, that in almost all cases such a wave group disappears in infinitely short time and therefore cannot possibly represent a real particle. Schrödinger also observed that in the many-electron problem, the interpretation he originally had in mind is necessarily invalid in ordinary space: “*ψψ̄* is a sort of weight function in the configuration space of the system.”

Shortly afterward Max Born interpreted *ψψ̄* as a probability, a view that Schrödinger considered a complete misinterpretation of his theory. From this time on, quantum theory developed in a way wholly different from the one Schrödinger had foreseen. In 1927 Heisenberg and Bohr succeeded in establishing, on a statistical foundation, an independent and consistent interpretation,” Schrödinger was “copenhagen interpretation.” Schrödinger was “concerned and disappointed” that this “transcendental, almost psychical interpretation of the wave phenomena” had become “the almost universally accepted dogma.” Schrödinger never changed his attitude on this subject, repeatedly defending the notion of “the electron as wave” and seeking to eleborate it without having recourse to the idea of “the electron as particle.”

In 1927 Schrödinger accepted the prestigious offer, which had been declined by Arnold Sommerfeld, to succeed Max Plank in the chair of theoretical physics at the University of Berlin. At the same time he became a member of the Prussian Academy of Sciences. The University of Zurich vainly sought to persuade him to stay, offering him, among other inducements, a double professorship jointly with the Eidgenödinger Technische Hochschule. Schrodinger was content in Zurich, despite occasional complaints; and his stay there had been very fruitful for the development of his scientific thought. Clearly, however, the city could not compete with Berlin, where, in the truest sense of the pharase, “physics was done. “Berlin. with its two universities, the Kaiser Wilhelm Institute, the Physikalisch-Techische Reichsanstalt, and numerous industrial laboratories, offered the possibility of contact with a large number of first-rate physicists and chemists. Still, Schrödinger did not find it easy to make the decision. It was Max Plank who finally brought the vacillating Schrödinger to Berlin with the words: “It would make me happy” —as Schrödinger himself recorded in the Planck family guest book.

Although Schrödinger was extremely fond of nature, especially the Alps, and dreaded the prospect of living in a big city, he very much enjoyed his years in Berlin. He developed a close friendship with Planck, whose scientific and philosophical views were similar to his own. After the “wandering years from 1920 to 1927,” this time of his life was “the very beautiful teaching and learning period.”

In 1933 Schrödinger was deeply outraged at the new regime and its dismissal of outstandingly qualified scientists. Frederick A.Lindemann (later Viscount Cherwell) offered him the support of Imperial Chemical Industries; and after a summer vacation in Wolkenstein in the Grödenertal (Val Gardena), where he had a depressing meeting with Born and Weyl, Schrödinger moved to Oxford at the beginning of November. The fifth day after his arrival, he was accepted as a fellow of Magdalen College. At the same time the *Times* of London called his hotel to tell him that he had been awarded the Nobel Prize in physics for 1933, jointly with P. A. M. Dirac.

At Oxford, Schrödinger gradually became so homesick for Austria that he allowed himself to be persuaded to accept a post at Graz in the winter semester of 1936–1937. After the *Anschluss* he was subjected to strong pressure from the National Socialists, who had not forgotten his emigration from Germany in 1933. His friends at Oxford observed his difficulties with great concern.

As early as May 1938 Eamon de Valera, who had once been professor of mathematics at the University of Dublin, attempted to find a way of bringing Schrödinger to Ireland. By the time Schrödinger was dismissed, without notice, from his position at Graz on 1 September 1938, the first steps had already been taken. Fortunately, Schrödinger had been left his passport and was able to depart unhindered, although with only a small amount of baggage and no money. Passing through Rome and Geneva, he first returned to Oxford. De Valera had a law passed in the Irish Parliament establishing the Dublin Institute for Advanced Studies; but in order to keep busy until it opened, Schrödinger accepted a guest professorship at the Francqui Foundation in Ghent.

At the beginning of September 1939, Schrödinger, as a German émigré, suddenly found himself an enemy alien: but once more de Valera came to his assistance, Through the Irish high commissioner in Great Britain, he arranged for a letter of safe conduct to be issued for Schrödinger, who on 5 October 1939 passed through England on his way to Dublin with a transit visa valid for twenty-four hours. Schrödinger spent the next seventeen years in the Irish capital, where he was able to work in his new position undisturbed by external events. He later called these years of exile “a very, very beautiful time. Otherwise I would have never gotten to know and learned to love this beautiful island of Ireland. It is impossible to imagine what would have happened if, instead, I had been in Graz for these seventeen years.”

The new Institute for Advanced Studies consisted of two sections, theoretical physics and Celtic languages, both located in a former townhouse on Merrion Square in Dublin. Young physicists from all over the world were given stipends enabling them to spend one or two years there. On the average there were ten to fifteen scholars in residence. Among them were Walter Thirring, Friedrich Mautner, Bruno Berdotti, and H. E. Peng. Like many of the others, Peng had previously worked with Max Born at Edinburgh. The yearly “summer school” in Dublin became famous as an informal gathering for the discussion of current problems of physics. Born and Dirac were frequent participants, and de Valera often came too.

In the years after his departure from Germany, Schrödinger published many works on the application and statistical interpretation of wave mechanics, on the mathematical character of the new statistics, and on its relationship to the statistical theory of heat. He also dealt with questions concerning general relativity, notably the relativistic treatment of wave fields, in contradistinction to the initial, nonrelativistic formulation of wave mechanics. In addition he wrote on a number of cosmological problems. Schrödinger, however, devoted an especially fervent effort, as did Einstein in his later years, to expanding the latter’s theory of gravitation into a “unified field theory,” the metric determination of which was to be established from a consideration of all the known forces between particles.

In his last creative period Schrödinger turned to a thorough study of the foundations of physics and their implications for philosophy and for the development of a world view. He wrote a number of studies on this subject in book form, most of them appearing first in English and then in German translation. It becomes particularly evident from the posthumously published *Meine Weltansicht* that Schrödinger was greatly concerned with the ancient Indian Philosophy of life (Vedanta), which had led him to concepts that closely approximate Albert Schweitzer’s “reverence for life.” In “What Is Life?” Schrödinger points out why physics had amassed so little empirical evidence that might be applicable to the study of cell development: a periodic crystals, in terms of which a gene should be considered, had not been investigated. But according to Delbrück’s model, quantum physics made it possible to understand general persistence as well as the case of spontaneous mutation. Schrödinger was convinced that the biological process of growth could also be conceived on the basis of quantum theory according to the schema “order out of order.” His analysis is outdated today: but during his lifetime it exerted enormous appeal among physicists (as Francis Crick corroborated) and induced many young people to study biology. Thus the great advances of molecular biology are indirectly linked to Schrödinger. He was a master of exposition, and Arnold Sommerfeld even spoke of a special “Schrödinger style.” Schrödinger wrote and spoke four modern languages (as well as Greek and Latin), translated various items, and published a volume of poertry—while continuing to bestow great care on the preparation of his lectures, as is evident from their exceptional accuracy. To keep up this pace he required a marked alternation of intensely productive periods with creative pauses.

Soon after the end of the war, Austria tried to convince Schrödinger to return home. Even the president, Karl Renner, personally intervened in 1946; but Schrödinger was not willing to return while Vienna was under Soviet occupation. In the succeeding years he often visited the Tirol with his wife, but he did not return definitively until 1956, when he was given his own chair at the University of Vienna. A year later he turned seventy, the customary retirement age in Austria but lectured for a further year (*Ehrenjahr*).

In his last years Austria honored Schrödinger with a lavish display of gratitude and recognition. Immediately after his return he received the prize of the city of Vienna. The national government endowed a prize bearing Schrödinger’s name, to be awarded by the Austrian Academy of Sciences, and Schrödinger wasits first recipient. In 1957 he was awarded the Austrian Medal for Arts and Science. He wrote that “Austria had treated me generously in every respect, and thus my academic career ended happily at the same Physics Institute where it had begun.”

On 27 May 1957 Schrödinger was accepted into the German order *Pour le mérite*. He was also granted honorary doctorates from a number of universities and was a member of many scientific associations, including the Pontifical Academy of Sciences, the Royal Society of London, the Prussian (later German) Academy of Sciences. In 1957 Schrödinger survived an illness that threatened his life, and he never fully recovered his health. he died on 4 January 1961 and is buried in the small village of Alpbach, in his beloved Tirolean mountains.

## BIBLIOGRAPHY

I. Original Works. Schrödinger’s important papers on wave mechanics are reprinted in *Abhandlungen zur Wellenmechanik* (Leipzig, 1927; 2nd ed., 1928): and *Diei Wellenmechanik*, vol. 3 of Dokumente der Naturwissenschaft (Stuttgart, 1963), which contains an extensive bibliography compiled by E. E. Koch of Schrödinger’s writings(pp. 193–199).

Some important correspondence is in Karl Przibram, ed., *Schrödinger. Einstein. Lorentz, Briefe zur Wellenmechanik* (Vienna, 1963), also translated into English by Martin J. Klein as *Letters on Wave Mechanics* (New York, 1967), which does not, however, contain Schrödinger’s letter to Enstein (28 Apr. 1926). Unpublished letters to Arnold Sommerfeld are at the Sommerfeld estate in the library at the Deutsches Museum. Munich. Two letters to Hermann Weyl were published by Johannes Gerber in *Archive for History of Exact Sciences*, **5** (1969), 412–416. The sources of other letters to and from Schrödinger are in T. S. Kuhn *et al., Sources for History of Quantum Physics. An Inventory and Report* (Phyladelphia, 1967), 83–86.

II. Secondary Literature. See Johannes Gerber, “Geschichte der Wellenmechanik,” in *Archive for History of Exact Sciences*, **5** (1969), 349–416: Armin Hermann. “Erwin Schrödinger—eine Biographie,” in *Die Wellenmechanik* (see above), 173–192; Max Jammer. *The Conceptual Development of Quantum Mechanics* (New York, 1966), 236–280; Martin J. Klein, “Einstein and the Wave-Particle Duality,” in *Natural Philosopher*, **3** (1964), 1–49; V. V. Raman and Paul Forman, “Why Was It Schrödinger Who Developed de Broglie’s Ideas? in *Historical Studies in the Physical Sciences*, **1** (1969), 291–314; William T. Scott, *Erwin Schrödinger, an Introduction to His Writings* (Amherst, Mass., 1967): Robert Olby, “Schrödinger’s problems: what Is Life?” in *Journal of the Histry of Biology*, **4** (1971), 119–148).

Armin Hermann

# Schrödinger, Erwin (1887-1961)

# SchrÖdinger, Erwin (1887-1961)

*Austrian physicist*

Erwin Schrödinger shared the 1933 Nobel Prize for physics with English physicist Paul Dirac in recognition of his development of a wave equation describing the behavior of an electron in an **atom** . His theory was a consequence of French theoretical physicist Louis Victor Broglie's hypothesis that particles of matter might have properties that can be described by using wave functions. Schrödinger's wave equation provided a sound theoretical basis for the existence of electron orbitals (energy levels), which had been postulated on empirical grounds by Danish physicist **Niels Bohr** in 1913.

Schrödinger was born in Vienna, Austria. His father, Rudolf Schrödinger, enjoyed a wide range of interests, including painting and botany, and owned a successful oil cloth factory. Schrödinger's mother was the daughter of Alexander Bauer, a professor at the Technische Hochschule. For the first eleven years of his life, Schrödinger was taught at home. Though a tutor came on a regular basis, Schrödinger's most important instructor was his father, whom he described as a "friend, teacher, and tireless partner in conversation," as Armin Hermann quoted in *Dictionary of Scientific Biography*. From his father, Schrödinger also developed a wide range of academic interests, including not only mathematics and science but also grammar and poetry. In 1898, he entered the Akademische Gymnasium in Vienna to complete his pre-college studies.

Having graduated from the Gymnasium in 1906, Schrödinger entered the University of Vienna. By all accounts, the most powerful influence on him there was Friedrich Hasenöhrl, a brilliant young physicist who was killed in World War I a decade later. Schrödinger was an avid student of Hasenöhrl's for the full five years he was enrolled at Vienna. He held his teacher in such high esteem that he was later to remark at the 1933 Nobel Prize ceremonies that, if Hasenöhrl had not been killed in the war, it would have been Hasenöhrl, not Schrödinger, being honored in Stockholm.

Schrödinger was awarded his Ph.D. in physics in 1910, and was immediately offered a position at the University's Second Physics Institute, where he carried out research on a number of problems involving, among other topics, **magnetism** and dielectrics. He held this post until the outbreak of World War I, at which time he became an artillery officer assigned to the Italian front. As the War drew to a close, Schrödinger looked forward to an appointment as professor of theoretical physics at the University of Czernowitz, located in modern-day Ukraine. However, those plans were foiled with the disintegration of the Austro-Hungarian Empire, and Schrödinger was forced to return to the Second Physics Institute.

During his second tenure at the Institute, on April 6, 1920, Schrödinger married Annemarie Bertel, whom he had met prior to the War. Not long after his marriage, Schrödinger accepted an appointment as assistant to Max Wien in Jena, but remained there only four months. He then moved on to the Technische Hochschule in Stuttgart. Once again, he stayed only briefly—a single semester—before resigning his post and going on to the University of Breslau. He received yet another opportunity to move after being at the University for only a short time: he was offered the chair in theoretical physics at the University of Zürich in late 1921.

The six years that Schrödinger spend at Zürich were probably the most productive of his scientific career. At first, his work dealt with fairly traditional topics; one paper of particular practical interest reported his studies on the relationship between red-green and blue-yellow color blindness. Schrödinger's first interest in the problem of wave mechanics did not arise until 1925. A year earlier, de Broglie had announced his hypothesis of the existence of matter waves, a concept that few physicists were ready to accept. Schrödinger read about de Broglie's hypothesis in a footnote to a paper by American physicist **Albert Einstein** , one of the few scientists who did believe in de Broglie's ideas.

Schrödinger began to consider the possibility of expressing the movement of an electron in an atom in terms of a wave. He adopted the premise that an electron can travel around the nucleus only in a standing wave (that is, in a pattern described by a whole number of wavelengths). He looked for a mathematical equation that would describe the position of such "permitted" orbits. By January of 1926, he was ready to publish the first of four papers describing the results of this research. He had found a second order partial differential equation that met the conditions of his initial assumptions. The equation specified certain orbitals (energy levels) outside the nucleus where an electron wave with a whole number of wavelengths could be found. These orbitals corresponded precisely to the orbitals that Bohr had proposed on purely empirical grounds thirteen years earlier. The wave equation provided a sound theoretical basis for an atomic model that had originally been derived purely on the basis of experimental observations. In addition, the wave equation allowed the theoretical calculation of energy changes that occur when an electron moves from one permitted orbital to a higher or lower one. These energy changes conformed to those actually observed in spectroscopic measurements. The equation also explained why electrons cannot exist in regions between Bohr orbitals since only non-whole number wavelengths (and, therefore, non-permitted waves) can exist there.

After producing unsatisfactory results using relativistic corrections in his computations, Schrödinger decided to work with non-relativistic electron waves in his derivations. The results he obtained in this way agreed with experimental observations and he announced them in his early 1926 papers. The equation he published in these papers became known as "the Schrödinger wave equation" or simply "the wave equation." The wave equation was the second theoretical mechanism proposed for describing electrons in an atom, the first being German physicist Werner Karl Heisenberg's matrix mechanics. For most physicists, Schrödinger's approach was preferable since it lent itself to a physical, rather than strictly mathematical, interpretation. As it turned out, Schrödinger was soon able to show that wave mechanics and matrix mechanics are mathematically identical.

In 1927, Schrödinger was presented with a difficult career choice. He was offered the prestigious chair of theoretical physics at the University of Berlin left open by German physicist Max Planck's retirement. The position was arguably the most desirable in all of theoretical physics, at least in the German-speaking world; Berlin was the center of the newest and most exciting research in the field. Though Schrödinger disliked the hurried environment of a large city, preferring the peacefulness of his native Austrian Alps, he did accept the position.

Hermann quoted Schrödinger as calling the next six years a "very beautiful teaching and learning period." That period came to an ugly conclusion, however, with the rise of National Socialism in Germany. Having witnessed the dismissal of outstanding colleagues by the new regime, Schrödinger decided to leave Germany and accept an appointment at Magdalene College, Oxford, in England. In the same week he took up his new post he was notified that he had been awarded the 1933 Nobel Prize for physics with Dirac.

Schrödinger's stay at Oxford lasted only three years; then, he decided to take an opportunity to return to his native Austria and accept a position at the University of Graz. Unfortunately, he was dismissed from the University shortly after German leader Adolf Hitler's invasion of Austria in 1938, but Eamon de Valera, the Prime Minister of Eire and a mathematician, was able to have the University of Dublin establish a new Institute for Advanced Studies and secure an appointment for Schrödinger there.

In September, 1939, Schrödinger left Austria with few belongings and no money and immigrated to Ireland. He remained in Dublin for the next seventeen years, during which time he turned to philosophical questions such as the theoretical foundations of physics and the relationship between the physical and biological sciences. During this period, he wrote one of the most influential books in twentieth-century science, *What Is Life?* In this book, Schrödinger argued that the fundamental nature of living organisms could probably be studied and understood in terms of physical principles, particularly those of quantum mechanics. The book was later to be read by and become a powerful influence on the thought of the founders of modern molecular biology.

After World War II, Austria attempted to lure Schrödinger home. As long as the nation was under Soviet occupation, however, he resisted offers to return. Finally, in 1956, he accepted a special chair position at the University of Vienna and returned to the city of his birth. He became ill about a year after he settled in Vienna, however, and never fully recovered his health. He died in 1961, in the Alpine town of Alpbach, Austria, where he is buried.

Schrödinger received a number of honors and awards during his lifetime, including election into the Royal Society, the Prussian Academy of Sciences, the Austrian Academy of Sciences, and the Pontifical Academy of Sciences. He also retained his love for the arts throughout his life, becoming proficient in four modern languages in addition to Greek and Latin. He published a book of poetry and became skilled as a sculptor.

** See also ** Quantum electrodynamics (QED); Quantum theory and mechanics

# Erwin Schrödinger

# Erwin Schrödinger

The Austrian physicist Erwin Schrödinger (1887-1961) was the founder of wave mechanics and described the quantum behavior of electrons.

For nearly 5 decades, Erwin Schrödinger, one of the most creative theoretical physicists of the 20th century, contributed papers to the scientific literature. Yet, from the start, his intellectual life was broadly based. He illustrated the breadth of his interests when he described how he intended to fulfill the duties of a professorship he expected to receive in 1918 at Czernowitz, Austria: "I was prepared to do a good job lecturing on theoretical physics … but for the rest, to devote myself to philosophy, being deeply imbued at the time with the writings of Spinoza, Schopenhauer, Mach, Richard Semon and Richard Avenarius." This professorship did not materialize. Nevertheless, throughout his life his philosophical concerns came to the surface, principally because he recognized that physics alone cannot provide an answer to Plotinus's ancient question, "And we, who are we, anyway?" Schrödinger's life was unified by his search for an answer to that simple but profound question.

Schrödinger was born on Aug. 12, 1887, in Vienna, the son of a successful and cultured businessman. In 1906 he entered the University of Vienna, where he was most stimulated by the experimental physicist Franz Exner and the theoretical physicist Fritz Hasenöhrl. After Schrödinger completed his doctoral degree in 1910, he remained as an assistant to Exner. In that capacity he explored various problems, many in solid-state physics.

In 1914 Schrödinger became privatdozent at Vienna but almost immediately found himself serving as an artillery officer in Italy. Shortly after he married Annamaria Bertel in 1920, he went to the University of Jena as an assistant to Max Wien. Within the next year he was called, first as associate professor to the Technische Hochschule in Stuttgart, then as full professor to the University of Breslau, and finally as full professor to the University of Zurich. His years at Zurich (1921-1927) were, scientifically speaking, the most productive in his career.

## Discovery of Wave Mechanics

In the immediate post-World War I years, Schrödinger worked on a variety of problems in different areas of physics: general relativity, statistical mechanics, radiation theory, the theory of colors, solid-state physics, and atomic spectroscopy. Some of his results are of great historical interest but have been superseded by new insights; others have remained of permanent interest. All of this work was but a prelude to those famous 2 months in 1925/1926, when, in an outburst of genius, he discovered wave mechanics.

When Schrödinger learned of Louis de Broglie's "matter-wave" hypothesis, he immediately tried to use it to explain the bright line spectrum emitted by the hydrogen atom; that is, he tried to apply it to the case of a single electron electrically "bound" to a proton. The results of his investigations—the wave equation he postulated and to which he applied the appropriate "boundary conditions"— were not in agreement with experiment. Discouraged, he put the work aside for some months—until one day in late 1925 the thought struck him that perhaps he should go against his instincts and not take account of the relativistic mass increase of the electron. The results were in striking agreement with experiment! Interestingly, it is now known that even Schrödinger's first, relativistic treatment of the problem is essentially correct—earlier, he had simply not taken account of the "spin" of the electron, a concept unknown to him at the time.

The nonrelativistic wave equation that Schrödinger assumed to govern the behavior of the electron in the hydrogen atom was of course the equation now universally known as the Schrödinger wave equation, the fundamental equation of wave mechanics. In less than 2 months he discovered his equation and began applying his elegant and beautiful theory to enough physical situations to carry complete conviction of its correctness. The capstone of his achievements was his proof of the logical equivalence of wave mechanics and "matrix mechanics," the latter discovered almost simultaneously by Werner Heisenberg in 1926.

## Later Scientific Work

In 1927 Schrödinger became Max Planck's successor at the University of Berlin, where he remained until the political events of 1933 and the accompanying anti-Semitic attacks on many of his colleagues forced him, as a matter of conscience, to resign his position. That year he received the Nobel Prize in physics, sharing it with Paul Dirac.

Schrödinger was a fellow at Oxford University from 1933 to 1936, when he accepted a professorship at the University of Graz. After Hitler annexed Austria in 1938, Schrödinger's outspoken anti-Nazism forced him to flee to Italy. As a member of the Pontifical Academy in Rome, he was reasonably safe and began to explore an idea communicated to him earlier by Eamon De Valera, a mathematician who at the time was also president of the Irish Republic, to establish a research institute in Dublin modeled after the Institute for Advanced Study in Princeton. Schrödinger went to Dublin in 1939 as director of the institute's School of Theoretical Physics. By the time he left Dublin in 1956 for Vienna (where a special chair in theoretical physics was created for him), his health was badly damaged and his productive life in physics was over.

During the preceding 3 decades, however, Schrödinger had continued to contribute to the development of quantum theory. He explored the theory of the Compton effect and potential barrier-penetration problems, and he developed the elegant factorization ("ladder operator") technique for generating solutions to the Schrödinger equation for some particular problems. In 1930 he demonstrated that a Dirac electron traveling in free space has superimposed on its motion a very small oscillatory motion, or *Zitterbewegung,* an insight which was subsequently of considerable theoretical importance for certain studies. Schrödinger carried out studies on relativity, cosmology, the unified field theory, meson physics, counter (detector) statistics, and statistical mechanics. He rarely worked with a colleague or student. Like Albert Einstein, he was a "horse for single harness" whose influence was disseminated and perpetuated not by a band of devoted followers but, rather, by his extensive writings.

## Humanistic Concerns

Schrödinger was always deeply concerned with philosophical questions—not only those that pertain to scientific issues but also those that pertain to essentially humanistic issues. The fundamental reason for his concern with these issues was his full recognition of the limitations of science. He was convinced, for example, that Heisenberg's uncertainty principle has nothing whatsoever to do with the ageold question of human free will. He believed that to illuminate questions such as these—to obtain a complete world picture—one requires the union of all knowledge, the insights achieved in all disciplines.

Schrödinger's quest to understand the nature of science and self led him to the study of history, particularly ancient history. He regarded Thales of Miletus as the first scientist because of Thales's profound insight that nature is understandable or comprehensible and not characterized by a capricious interplay of superstitions and uncontrollable forces. A century later Heraclitus concluded that this comprehensibility is possible only if the world is so constructed as to appear the same to all sane, waking, persons—only if there exists a "world in common."

According to Schrödinger, this world in common is discovered through observation in combination with insights of a metaphysical nature—hunches, spontaneous creative thought, and the like—that guide the interpretation of the observations. He believed that this world in common, to be comprehensible, had to be to a large degree a deterministic, causal world. Chance elements could enter only through the "intersection of causal chains"; these chance elements are precisely the sort of events that scientists prefer not to talk about, but that theologians and philosophers are profoundly interested in. Thus, once again, Schrödinger was led to conclude that the only way to achieve a complete world picture is to take account of nonscientific as well as scientific knowledge. He felt this to be particularly true when discussing questions like the origin and nature of life, as well as the profoundly interesting role that chance played in Darwinian evolution.

Schrödinger died in Vienna on Jan. 4, 1961.

## Further Reading

Schrödinger discussed his work in his Nobel lecture, reprinted in *Nobel Lectures in Physics,* vol. 2 (1965). A collection of letters exchanged by Schrödinger, Einstein, Planck, and Hendrik Lorentz is *Letters on Wave Mechanics,* edited by K. Przibram and translated by M. J. Klein (1967). The most complete source of information on Schrödinger and his work is William T. Scott, *Erwin Schrödinger: An Introduction to His Writings* (1967), which includes a bibliography. An obituary by Walter Heitler is in the *Biographical Memoirs of Fellows of the Royal Society of London,* vol. 7 (1961). For the historical significance of Schrödinger's work see Max Jammer, *The Conceptual Development of Quantum Mechanics* (1966).

## Additional Sources

Mehra, Jagdish, *Erwin Schrödinger and the rise of wave mechanics,* New York: Springer-Verlag, 1987.

Moore, Walter John, *A life of Erwin Schrödinger,* Cambridge;

New York: Cambridge University Press, 1994. Moore, Walter John, *Schrödinger, life and thought,* Cambridge;New York: Cambridge University Press, 1989.

Schrödinger, Erwin, *What is life?: the physical aspect of the living cell; with, Mind and matter; & Autobiographical sketches,* Cambridge; New York: Cambridge University Press, 1992. □

# Schrödinger, Erwin

# Schrödinger, Erwin

**AUSTRIAN THEORETICAL PHYSICIST1887–1961**

Erwin Schrödinger was born in Vienna, Austria, in 1887. In 1906 he entered the University of Vienna with the intention of studying statistical thermodynamics with the mathematician and physicist Ludwig Boltzmann. Unfortunately it was the year Boltzmann committed suicide, and Schrödinger studied under Boltzmann's successor, Fritz Hasenöhrl. Schrödinger received his doctorate in 1910 for a dissertation on electrical conduction. The next four years were spent as an assistant instructor in experimental physics at the University of Vienna. In 1914 he was drafted to serve in the Austro-Hungarian army and fought on the side of Germany during World War I. In 1917 he returned to his former position in Vienna. In the aftermath of several research successes, Schrödinger found himself to be in great demand, and he accepted, one right after the other, faculty positions at the Universities of Jena, Stuttgart, and Breslau. Finally, in late 1921 he accepted the chair in **theoretical physics** at the University of Zurich (in Switzerland). Although his stay there was relatively short (six years), it was there that he published his most significant work—in quantum statistics, the dynamics of crystal lattices, the theory of color vision, and quantum theory.

Schrödinger's work in quantum theory resulted in the creation of a new scientific discipline—wave mechanics, which has as its centerpiece the Schrödinger wave equation, explained in a series of four papers published in 1926. This equation and the later relativistic versions are considered by many scientists to have the same central importance to molecular quantum mechanics as Newton's laws of motion have to large-scale classical mechanics.

Schrödinger began to search for a wave equation in 1925 after reading a paper by Albert Einstein about Louis de Broglie's ideas that matter could possess both wave and particle properties simultaneously, as expressed in the de Broglie equation relating the wavelength of a matter wave to its momentum. Schrödinger demonstrated that the de Broglie equation could be generalized so as to apply to particles such as electrons in atoms. The Schrödinger equation is a wave equation that explains the properties and behavior of all types of submicroscopic particles with small masses and that are in the presence of electric and magnetic fields. Schrödinger's work was immediately accepted worldwide, and he received a call to accept the challenge of succeeding Max Planck in the department of theoretical physics at the University of Berlin. He stayed until 1933, but by that time he had become so outraged by the German government's treatment of Jewish scientists that he accepted a position at Oxford University in England, just before he was informed that he had been awarded the 1933 Nobel Prize in physics for his development of wave mechanics. For the next seven years (during which time a return to Vienna would have been most difficult), he accepted several temporary appointments. In 1941 he became director of the School of Theoretical Physics at the Dublin Institute for Advanced Studies (in Ireland). There he worked mainly on unified field theory.

He also published a number of books. Of these, *What Is Life? The Physical Aspect of the Living Cell* is credited with having persuaded physicists to take an interest in the problems of biology. It is also credited with having attracted many young people to the new field of molecular biology. For instance, James Watson, one of the discoverers of the structure and function of **DNA** , stated that, from the moment he read the book, he "became polarized toward finding out the secret of the gene."

In 1955 Austria became free of Soviet occupation, and Schrödinger returned to the University of Vienna, where he received many honors as Austria's greatest living scientist. Schrödinger retired in 1958 and died in 1961.

see also de Broglie, Louis; Quantum Chemistry; Watson, James Dewey.

*John E. Bloor*

## Bibliography

McMurray, Emily J., ed. (1995). *Notable Twentieth-Century Scientists.* Detroit: Gale Research.

Mehra, Jagdish, and Rechenberg, Helmut (1987). *The Historical Development of Quantum Theory,* Vol. 5. *Part 2: The Creation of Wave Mechanics; Early Response and Applications, 1925–1926.* New York: Springer-Verlag.

Moore, Walter (1994). *A Life of Erwin Schrödinger.* New York: Cambridge University Press.

# Erwin Schrödinger

# Erwin Schrödinger

**1887-1961**

**Austrian Physicist**

Best known for his wave equation and a thought experiment involving an imaginary cat, Erwin Schrödinger contributed to a variety of disciplines from biology to philosophy. Like so many of his generation, his life and career were shaped heavily by two world wars and the political divisions of Europe.

Born and raised in Vienna, Austria, Schrödinger was the son of a frustrated scientist who was determined that his son would have every possible opportunity. Until the age of 11 Erwin had a private tutor, then he entered the Akademisches Gymnasium (approximately a high school) gaining a broad education, excelling at chemistry and mathematics, but also enjoying poetry, drama, and grammar, and becoming fluent in German, English, French, and Spanish. He concentrated first on chemistry, then on Italian painting, and published several papers in botany.

In 1906 he entered the University of Vienna, where he excelled in theoretical and experimental physics. Upon graduating Schrödinger did a year of military service. He then continued research in physics until the outbreak of World War I, in which he served as an artillery officer on the Italian Front.

During the war Schrödinger's favorite teacher, Fritz Hasenöhrl (1874-1916) died. Schrödinger decided to teach at Hasenöhrl's old school in Czernowitz to honor his memory. However, the city of Czernowitz (later Chernovtsy) was taken from Austria as war reparations by Russia, making this impossible. Looking back, Schrödinger wrote, "I had to stick to theoretical physics, and, to my astonishment, something occasionally emerged from it."

In 1920 he married and received a good research position in Germany. He did important work on color theory and on the statistical thermodynamics of ideal gases. However, he was unhappy in his marriage, and his research dried up. In 1925 he wrote a very introspective account of his philosophy of life.

1926 was a turning point for Schrödinger. He was inspired by Louis de Broglie (1892-1987), whose work suggested that waves and particles could be considered interchangeable (wave-particle duality). An affair with a young woman, the first of several, provided another inspiration. Secluded in a holiday villa with his new companion, he would place pearls in his ears to block out noise and work for hours uninterrupted. The six major papers that came from this year had far-reaching implications for both physics and chemistry.

Schrödinger proposed a wave interpretation of the distribution of electrons in an atom. His wave equation was entirely theoretically based, yet gave results that agreed with experimental observations. Schrödinger felt his wave mechanics offered a more appealing approach to quantum physics, providing a way of visualizing the atom, rather than the abstract statistics of other methods.

In 1933 he received the Nobel Prize in physics, shared with Paul Dirac (1902-1984). That same year the Nazi party came to power in Germany, and Schrödinger left for Oxford, England. He was lured back to Austria, but in 1938 it was annexed by Nazi Germany, and he was forced to flee, ending up in Dublin, Ireland, where he stayed until 1955.

Never entirely happy in the direction quantum physics developed, Schrödinger often found himself at odds with other scientists. He offered many criticisms of quantum interpretations, the most famous being a thought experiment known as Schrödinger's Cat, in which a quantum event produces strange results in the observable world.

He published numerous works in physics, but also a short volume of poetry, and an influential book on biology, *What is Life* (1944). Schrödinger wrote about his career, "In my scientific work (and moreover also in my life) I have never followed one main line, one program defining a direction for a long time."

**DAVID TULLOCH**

# Schrödinger, Erwin

**Schrödinger, Erwin** (1887–1961) Austrian physicist, who formulated a quantum mechanical wave equation. He went on to found the science of quantum wave mechanics and shared the 1933 Nobel Prize in physics with the English physicist Paul Dirac. The wave equation was based on a suggestion by the French physicist Louis de Broglie that moving particles have a wave-like nature.

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**Erwin Schrodinger**