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Slater, John Clarke

SLATER, JOHN CLARKE

(b. Oak Park, Illinois, 22 December 1900; d. Sanibel Island, Florida, 25 July 1976)

theoretical physics, quantum mechanics.

John Slater was one of the few physicists trained in America in the 1920’s to specialize in theoretical physics and to contribute to both the development of quantum mechanics and its application to a wide range of particular phenomena. The theme of his career was to explain observable phenomena using quantum-mechanical models. As a prolific writer of textbooks and research papers, as a teacher, as chairman of the physics department and later institute professor at the Massachusetts Institute of Technology (MIT), and as graduate research professor at the University of Florida, Slater channeled large numbers of workers into the burgeoning areas of molecular and solid-state theory. He was among those responsible for the emergence of American theoretical physics between the two world wars, and for bringing American solid-state physics into a leading position in the international arena.

Slater grew up in an academically oriented home. When he was a baby his father, John Rothwell Slater, a Harvard graduate, was a doctoral student at the University of Chicago. In 1904 the family moved to Rochester, New York, where Slater’s father joined the English department at the university, a department he later became the head of. In his boyhood Slater was very much interested in mathematics and in examining such devices as electrical motors and lamps. His father, whose home library included physics classics like A. A. Michelson’s Light Waves and Their Uses, strongly encouraged his son’s scientific bent and in later years would habitually enclose clippings from Scientific American in his letters. Slater’s high school interests also included watercolor painting, architecture, and printing in his attic print shop.

Slater abandoned his plan to attend Harvard College when it became clear that the United States would enter World War I. He remained at home, entering the University of Rochester in 1917, and completed his undergraduate work in three years. Majoring in science, he took his A.B. in 1920. His research in atomic and molecular physics began during his senior year at Rochester, where, as an assistant in the physics laboratory, he conducted a special experimental honors thesis, examining the relationship between change of pressure and the intensities of the Balmer spectral lines in hydrogen, a project inspired by his reading of Niels Bohr’s classic 1913 paper on atomic theory.

Slater then entered Harvard’s graduate school in physics, from which he took his doctorate in June 1923. He was introduced there to the major problems at the frontiers of quantum theory in Edwin C. Kemble’s course, one of the few in America then up to date in modern physics. Slater’s exposure to the philosophy of pragmatism in science, as an assistant to Percy W. Bridgman, appears to have had a lasting influence on him, for in his subsequent research Slater never strayed far from observable phenomena. Bridgman, who was then pioneering the study of phenomena at high pressures, supervised Slater’s doctoral thesis, an experimental investigation of the compressibility of alkali halide crystals. This research brought Slater into contact with fundamental problems of the solid state, which were to challenge him throughout his career. For example, he realized that the existing theory was incapable of explaining the repulsive forces in solids that counter electrostatic attraction.

Slater decided to spend the year following the completion of his doctorate abroad, close to the revolutionary breakthroughs then being made in quantum theory. Supported by a Sheldon traveling fellowship from Harvard, he spent the fall of 1923 at the Cavendish Laboratory at Cambridge studying the theoretical problem of the breadth of spectral lines. He explored the picture, suggested previously by W. F. G. Swann and others, of an electromagnetic field that guides the light photons emitted by atoms, the energy density of the field determining the probability of finding a photon at a particular position. In a theory Slater developed in these months at Cambridge, the source of the electromagnetic field was identified as either the atoms oscillating in excited Bohr states, emitting electromagnetic waves at all the frequencies corresponding to transitions to lower Bohr states, or the oscillations produced by the impact of external radiation on the atom. Slater’s discussion of this theory with Bohr and Hans Kramers in December of that year in Copenhagen resulted in the celebrated joint Bohr-Kramers-Slater paper on the quantum theory of radiation, published in 1924. Historically this paper was to be a root of Werner Heisenberg’s matrix mechanics, despite its incorrect assumption, due to Bohr and Kramers, that the laws of energy and momentum conservation have only statistical validity. Bohr and Kramers gave the name virtual oscillators to the oscillations of the electrons corresponding to the possible transitions, disagreeing with young Slater that the photons accompanying these transitions have a simultaneous real existence. Slater never quite forgave Bohr and Kramers for thus distorting his original theory.

After returning to Harvard in June 1924, he worked further on the radiation problem, publishing early in 1925 a more consistent picture of how the oscillators determine the emission and absorption probabilities and underlining the real existence of the emitted photons, the energy conservation in the system of the atoms and photons, and the probabilistic relation between the intensity of the field and the motion of the photons. These ideas were at that time also being clarified in the work of Louis de Broglie. In one important work in 1925 Slater correlated the width of spectral lines with the reciprocal lifetime of stationary states; in another he almost arrived at the notion of spin, which soon afterward George Uhlenbeck and Samuel Goudsmit made explicit.

In 1926 Slater married Helen Frankenfeld, with whom he was to have three children: Louise Chapin, John Frederick, and Clarke Rothwell. The daughter of a minister in Rochester, Helen also studied at the University of Rochester. She graduated in 1925 with a major in English. After the marriage, she studied further in Boston, in a nursery training school, but she gave up her career plans when the children were born. Helen and John Slater hosted a large number of professional parties in their home. Their marriage ended in divorce in 1952.

In late 1926, studying the radiation problem in the context of the singly ionized hydrogen molecule, Slater extended Heisenberg’s recent analysis of helium, which had established the existence of symmetric and antisymmetric two-electron states, developing a picture of electrons moving between potential wells equivalent to what was later named “tunneling.” Addressing the problem of exchange effects in the helium atom, Slater returned to one of the questions raised by his doctoral thesis: Why are inert gas atoms relatively hard and impenetrable? The theme of accurate calculation of the wave functions and energies of many-electron atoms and molecules would be a major theme of his research for the next half-century.

Slater’s next major move in physics was to “slay the Gruppenpest,” the curse of having to use group theory to treat complex systems. In the mid-1920’s several workers, including Eugene Wigner, Friedrich Hund, Walter Heitler, and Hermann Weyl, were trying to extend the Heisenberg two-electron picture to many electrons using abstruse group theoretical methods, which many physicists of that period, including Slater, disliked intensely. Stimulated by Douglas R. Hartree’s 1928 work on the self-consistent field method for treating problems in atomic physics—an iterative method for calculating single-particle wave functions based on the recognition that the average fields felt by an electron depend on the states of all the other electrons, these states themselves being determined by the average field—Slater turned to a detailed examination of why the method was successful. This study culminated in Slater’s major 1929 paper on the theory of complex spectra, which presented for this problem a convenient determinantal alternative to the unwieldy group approach. Building on ideas developed by Paul A. M. Dirac, Heisenberg, Wolfgang Pauli, and Hund, Slater found that by setting up a many-electron function in the form of a determinantal antisymmetric combination of one-electron wave functions, he could achieve a self-consistent field wave function with the correct symmetry. Electron spin was explicitly included in the individual terms of the determinant. Slater also noted that Hartree’s expression for the potential of an atom could be derived by a variational approach, discovering independently of V. Fock what came to be called the Hartree-Fock method, a method improving the accuracy of Hartree’s original self-consistent field method by including electron exchange terms.

Slater visited Europe again between June 1929 and February 1930, with support from a Guggenheim Fellowship. He worked for most of this visit at the theoretical physics institutes of Heisenberg in Leipzig and Pauli in Zurich, which by this time had become the most active European centers for theoretical study of solids. Extending to many other cases his determinantal method, Slater also worked on the problem of cohesion in metals, demonstrating the close relationship between Hund’s molecular orbital method, which began with the assumption that an individual electron in a molecule moves in a potential arising from the nuclei and the average space charge of the other electrons, and the method of Heitler and Fritz London, which began by ignoring the interaction between the two electrons in the hydrogen molecule and treating their wave function as a product of two one-electron functions.

These methods Slater then applied to ferromagnetism. Heisenberg’s classic 1928 treatise on ferromagnetism was not mathematically rigorous and could not explain why ferromagnetism is found only in certain elements. Slater found, as did Felix Bloch independently, that the low-lying stationary states in which all but one of the atoms have parallel electron spins correspond to spin waves—the wavelike propagation through the system of a slight disturbance of the spin orientation from its equilibrium value. In studying a preprint of Bloch’s work (which already made use of the Slater determinants). Slater realized that the relation between the Heisenberg and Bloch approaches to ferromagnetism is analogous to the relation he had recently investigated between the Heitler-London and Hund molecular orbital approaches to molecular forces.

Slater’s characteristic quantitative approach to physics is well illustrated by his discovery that the root of ferromagnetism lies in the electron atomic 3d shell. Bloch had shown that in the limit of large internuclear separations the magnetic state has a lower energy than the nonmagnetic state. Slater proceeded to seek the electrons responsible for ferromagnetism in narrow partly filled bands formed of slightly overlapping atomic wave functions. Estimating the sizes of various unfilled shells of atoms in the periodic system, he showed that the 3d shell of the iron group elements was the narrowest unfilled band, a band sufficiently small that it becomes energetically favorable for spins to be oriented parallel: the magnitude of the energy decrease owing to quantum-mechanical exchange when spins are parallel exceeds the energy that must be added to the system to excite electrons above the energy levels occupied in the nonmagnetized ground state. This imbalance between the two energies enables spontaneous magnetization to occur. For cobalt, nickel, and particularly iron, all ferromagnetic, he found the ratio of the internuclear distance to the radii of the 3d shell orbital to be particularly high.

Shortly after returning to Harvard in the spring of 1930, Slater accepted an offer from Karl Compton, MIT’s new president, to head the MIT physics department. Under Slater’s direction the department expanded rapidly and broadened its scope. By concentrating on solid-state physics at a time when most American institutions were turning to nuclear physics, Slater enabled the MIT department to achieve first rank with a distinctive emphasis on solving problems of real materials using quantum mechanics.

With his students, Slater applied the determinantal method to many problems, including valence bonds. In a seminal paper published in 1931 Slater introduced the concept of “directed valence,” arrived at simultaneously by Linus Pauling; by constructing linear combinations of s and p waves he showed that wave functions could be made that project out in the direction of a bond. Not long afterward he was elected to the National Academy of Sciences, at the age of thirty-one.

The other emerging American effort in solid-state theory in the early 1930’s was the small group in the Princeton physics department surrounding Wigner, consisting primarily of postdoctoral and doctoral students (including Frederick Seitz, John Bardeen, and Conyers Herring). Compton’s wish that MIT and Princeton maintain close ties aided communication between these two groups in the 1930’s. Slater was particularly impressed by Wigner and Seitz’s classic paper in 1933 on the energy bands of sodium, laying out the first approximate method for calculating realistically the band structure of simple solids. Immediately recognizing that this work opened new paths, Slater extended the Wigner-Seitz method to the excited bands of metals, and with his students applied the technique to a series of particular solids, including copper, diamond, carbon, and sodium chloride. Slater surveyed the applications of the Wigner-Seitz method in an important article in the 1934 Reviews of Modern Physics, one of several reviews on the electron theory of metals to appear circa 1933 (the most extensive being that by Hans Bethe and Arnold Sommerfeld in the 1933 Handbuch der Physik). With powerful new quantum-mechanical concepts developed between 1927 and 1933 (including the Fermi sea, Bloch waves, and energy bands), Pauli, Sommerfeld, Heisenberg, Bloch, Rudolf Peierls, Alan Wilson, Slater, and others had resolved the outstanding dilemmas of the classical electron theory of metals and placed the theory of ideal metals and semiconductors on a sound intellectual foundation. The reviews circa 1933 enabled this fundamental theory to enter the graduate programs at leading physics institutions, providing the basic texts for training the first generation of physicists who referred to themselves as solid-state physicists. This generation faced the challenging problem of explaining the detailed properties and behavior of real, rather than ideal, solids.

Slater was one of the few physicists (another was his Harvard colleague and close friend John Van Vleck) who worked steadily in the solid-state area through this transition. Due to various circumstances—the displacement of Jewish physicists, a feeling that most of the fundamental problems other than superconductivity were solved, and the discovery of new and exciting phenomena and techniques in nuclear and particle physics—most of the contributors to solid-state theory were by 1933 redirecting their primary attention to nuclear physics and quantum electrodynamics. Fortunately, at just this time, several new workers, including Bardeen, Herring, and Seitz in the United States and Nevill Mott in England, were entering the study of the solid state, sharing Slater’s burden in establishing this new subfield of physics.

Slater students engaged in energy band calculations in the mid-1930’s included Harry M. Krutter, who studied the Wigner-Seitz method in relation to the Thomas-Fermi method for metals; George Kimball, who computed energy bands in diamond; and William Shockley, who studied sodium chloride. Slater applied the Wigner-Seitz method to ferromagnetism in 1936. Other concerns of Slater’s solid-state group in the late 1930’s included the determination of charge densities by summing over the occupied orbitals, calculating forces and energies by applying the Feynman-Hellmann theorem, and computing the potential and kinetic energies by using the virial theorem. Slater also turned to the study of localized excitations in crystals. In 1936, with Shockley, Slater developed a framework for a theory of the exciton; and in the spring of 1937 he worked out a useful relationship between the theory of excitons and Bloch’s 1929 theory of spin waves.

Slater continued to seek better methods of computing energy bands and in 1937 invented the “augmented-plane-wave method,” which expands wave functions in spherical harmonics and radial solutions within spheres surrounding the atoms, and in plane waves outside. Slater’s students, including Marvin Chodorow, tested this method on copper bands before World War II, but only in the 1950’s, with the help of digital computers, could large-scale application of the method be made. The group also explored extensively the “orthogonalized-plane-wave-method,” an alternative to the Slater augmented-plane-wave method developed by Herring in 1940 and applied first to computation of the energy bands of beryllium. In the method of orthogonalized plane waves, the wave function has been made orthogonal to the ion-core wave function so that there is no wave amplitude for ion-core levels (which are filled).

Slater’s principal concern during World War II—partly at MIT and partly as a member of the technical staff of the Bell Telephone Laboratories—was microwave radar, particularly the theory of the magnetron, which drew on mathematical techniques he had developed earlier while trying to understand the Meissner effect in superconductivity and the self-consistent field in atoms. Immediately after the war, Slater turned to rebuilding MIT’s physics department. Through his war work he sensed the possible physics applications of wartime technological developments, including microwaves, rapid electronics, digital computers, neutron beams, and the Collins cryostat (a compact helium liquefier enabling experiments to be conveniently carried out over long periods at temperatures as low as two degrees above absolute zero). He made a decided effort to apply these wartime advances in the postwar research program at MIT, for example in experimental studies of superconductivity and in building linear accelerators.

The invention of the first transistors in 1947 and 1948 set off a revolutionary expansion in the field of solid-state physics. Slater, stimulated by several solid-state conferences held in mid-1948, returned to active work in this field and set up MIT’s Solid-State and Molecular Theory Group (which a decade later would evolve into MIT’s Center for Materials Science and Engineering). The program included practical calculations employing Hartree-Fock, Wigner-Seitz, Thomas-Fermi-Dirac, and other methods, pioneering the use of digital computers in solving a variety of problems, including ferromagnetism, antiferromagnetism, binding energies, and energy bands. The MIT physics department also expanded its programs in X rays, acoustics, electronics, and optics, all fields of great interest to industry.

Attracted by the opportunity to explore neutron diffraction in the study of magnetic and other properties of the solid state. Slater accepted an appointment for the academic year 1951–1952 at Brookhaven National Laboratory. At this juncture he stepped down from the post he had held for twenty-one years as MIT’s physics department chairman and was appointed MIT’s first institute professor, a position which allowed him far more time for research, teaching, and travel, both in the United States and in Europe. In 1954 he married Rose Mooney, a physicist specializing in the study of crystals by X-ray diffraction.

In anticipation of his retirement in 1966 from MIT, Slater in 1964 transferred his base to the University of Florida in Gainesville, where he joined the Quantum Theory Project, set up by Per-Olov Löwdin. Until his retirement from his Florida position in June 1976, a month before his death, Slater continued, both individually and with students, to work intensively on theories of the detailed properties of real crystals. Slater particularly enjoyed these last years in Florida. He described the Florida department in his autobiography as congenial, and with its emphasis on just the problems in which he was most interested, the areas of solid-state physics and related fields, it reminded him of the MIT physics department in the years when he served as its head. He was awarded the Medal of Science in 1971. Slater wrote fourteen textbooks between 1933 and 1974—characteristically typing them himself, with little revision after the first draft—on theoretical physics, mechanics, electromagnetism, the quantum theory of atoms, molecules and solids, chemical physics, microwave transmission and electronics, energy bands, and self-consistent field methods. Slater’s roles as teacher of theoretical physics, quantum mechanics, and solid-state physics and as a prolific writer of textbooks useful to both the student and practicing physicist touched most of the physicists who worked in the five decades following the invention of quantum mechanics.

BIBLIOGRAPHY

I. Original Works. The most complete source for Slater’s life and works is the exceptionally well cataloged collection of letters, manuscripts, and other documents in the John Clarke Slater Papers at the American Philosophical Society Library in Philadelphia, Pennsylvania. A bibliography of Slater’s published works (including approximately 150 research papers and other articles, in addition to his textbooks and scientific autobiography) appears in Philip M. Morse. “John Clarke Slater, December 22, 1900–July 25, 1976,” in Biographical Memoirs National Academy of Sciences, 53 (1982), 297–321. Slater’s colorful scientific autobiography, Solid-State and Molecular Theory: A Scientific Biography (New York, 1975), offers his view of the developments in physics that impressed him most as he moved through his career. Partial autobiographical accounts are also included in “Quantum Physics in America Between the Wars,” in Procceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory: Symposium No. I. International Journal of Quantum Chemistry (1967), 1–23; and “The Current State of Solid-State and Molecular Theory,” ibid., 37–102. Many useful reflections on Slater’s career can be found in Slater’s oral history interviews with Thomas Kuhn and John H. Van Vleck on 3 October 1963, with, Kuhn on 8 October 1963, and with Charles Weiner on 23 February and 7 August 1970, all on file at the American Institute of Physics Center for History of Physics. New York City.

II. Secondary Literature. In addition to the biographical memoir by Philip M. Morse listed above, see P. Hoch (with contributions from K. Szymborski). “The Development of the Band Theory of Solids, 1933–1960,” in L. Hoddeson et al., eds., Out of the Crystal Maze (New York and Oxford, 1990); L. Hoddeson. G. Baym, and M. Eckert, “The Development of the Quantum-Mechanical Electron Theory of Metals: 1928–1933,” in Reviews of Modern Physics, 59 (1987), 287–327; Katherine Russell Sopka, Quantum Physics in America, 1920–1935 (diss., Harvard University, 1976).

Lillian Hoddeson

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