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London, Fritz

London, Fritz

(b. Breslau, Germany [now Wroclaw, Poland], 7 March 1900; d. Durham, North Carolina, 30 March 1954)

physics, theoretical chemistry.

Fritz London and his younger brother, Heinz, were the only children of Franz London, Privatdozent in mathematics at Breslau and later professor at Bonn, and Luise Hamburger, daughter of a linen manufacturer. The home atmosphere was that of a cultivated and prosperous liberal German-Jewish family, disturbed only by the premature death of Franz London m 1917. London attended high school at Bonn, where he received a classical education, and the universities of Bonn, Frankfurt, and Munich. His first academic interest was philosophy: in 1921 he received a doctorate summa cum laude at Munich for a dissertation on the theory of knowledge based on the symbolic methods of Piano, Russell, and Whitehead and their followers. He had done the work without supervision and entered it for the degree at the suggestion of G. Pander, to whom he had shown it for criticism. The philosophic bent remains noticeable throughout London’s work, which is characterized by a constant search for general principles and thorough exploration of the logical foundations of his chosen subjects. He was never a mere calculator. In 1939 he published jointly with Ernst Bauer a short monograph in French on the theory of measurement in quantum mechanics.

During the three years following publication of his dissertation London wrote two further philosophical papers and spent some time as a high school teacher in various parts of Germany, but in 1925 he returned to Munich to work in theoretical physics under Sommerfeld. He then held in succession appointments at Stuttgart with P. P. Ewald and at Zurich and Berlin with Schrödinger, In 1933 the Nazi persecution forced both London brothers to leave Germany. London spent two years at Oxford and two years in Paris at the Institute Henry Poincaré. In 1939 he was appointed professor of theoretical chemistry (later chemical physics) at Duke University, where he remained until his death. In 1929 he married the artist Edith Caspary. They had two children.

Between 1925 and 1934 London’s interests centered on spectroscopy and the new quantum mechanics, chiefly as applied to the chemical bond. His first scientific paper, written jointly with H. Hönl, was on the intensity rules for band spectra. In 1927 he and W. Hitler produced their classic quantum-mechanical treatment of the hydrogen molecule, “the greatest single contribution to the chemist’s conception of valence made since G, N. Lewis’ suggestion in 1916 that the chemical bond between two atoms consists of a pair of electrons held jointly by the two atoms.”1 Heitler and London set themselves the problem of determining the energy of a quantum mechanical system having two electrons in motion about two charged nuclei (protons). At large distances, with one electron orbiting each nucleus, the system is just a pair of hydrogen atoms; but when the nuclei are brought closer the forces between all four particles must be taken into account It had long been recognized that two atoms A, B, may combine as a stable molecule with separation of if the interatomic forces vary so as to make the total energy a minimum at that distance. A complete quantum mechanical calculation of the forces requires precise knowledge of the probability function for the distribution of electrons, which is exceedingly complicated, but Heitler and London were able to approximate the solution by means of an analytical technique developed in the theory of sound by Lord Raleigh. In a vibrating body, such as a bell, the energy associated with the lowest normal mode of vibration is a minimum. Any motion of slightly different form will have higher energy, but since it is near a minimal point, the increase in energy due to first-order deviations in motion is of the second order of small quantities. A rather good estimate of the energy of vibration may therefore be made from quite a crude approximation to the actual motion; and of any two approximate solutions the one yielding lower energy is nearer the truth. Rayleigh’s method supplies a guide for guesswork in the study of complex vibrating systems; equivalent ideas apply to the solution of Schrödingers wave equation in quantum mechanics. The first trial wave function used by Hitler and London for the hydrogen molecule was simply the known expression for one electron orbiting each nucleus, that being the exact solution at large distances where the interactions between the atoms are negligible. In this case the function probability of the two electrons 1, 2 being found in the same volume element of space is (by ordinary statistical theory) the product of their separate probabilities, and hence their joint wave function ψAB(1,2) from which the probabilities are determined is

where ψA(l) is the wave function for electron I orbiting atom A, and ψB(2) for electron 2 orbiting atom B. Insertion of ψB(1) into Schrödinger’s equation does yield an attractive force between the atoms at large distances and an energy minimum when they are separated by about 0.9 A°, but the calculated binding energy is far from the experimental value.

The next step hinged on a concept put forward in another connection by Heisenberg about a year earlier. Since in quantum mechanics the two electrons are indistinguishable, they may be supposed to change places without altering the system in any way, and a better approximation to the wave function will be

From (2) with the positive sign Heitler and London obtained an expression for the total energy WM of the molecule having the form

where WH is the ground state energy of an isolated hydrogen atom, e2rABthe electrostatic repulsion between the two nuclei, J,J’, K, K’, and Δ are various integrals, of which J can be interpreted as the net attraction between each electron cloud and the nucleus of the other atom, J’ the repulsion between the electron clouds, and K and K’ are the socalled exchange integrals whose meaning will be discussed below. The energy is substantially reduced, so by Rayleigh’s principle the function (2) is indeed a closer approximation than (1) to the real distribution. Figure 1 reproduces the calculated curve, which has a

pronounced minimum at an interatomic spacing 0,79 A and gives a binding energy of 3.14 electron volts, which may be compared with the experimental values 0.74 A and 4.72 ev. Finally, extending London’s earlier interest in the band spectra of molecules Heitler and London determined a vibrational frequency for the molecule from the curvature of the potential near the minimum and obtained a value of 4800 cm-1 as compared with the observed spectral frequency of 4318 cm-1.

Improvements in detail to the Heitler-London solution were soon made by others, chief being corrections for screening of the nuclei by the electron cloud (S. C. Wang), polarization of the charge cloud (N. Rosen), and the addition to equation (2) of terms describing ionic structures (S. Weinbaum). In J933 H. M. James and A. S. Coolidge gave a laborious investigation introducing the interelectronic distance r12 explicitly into the analysis and comparing results for variation functions with five, eleven, and thirteen terms. The calculations converged on values for the binding energy, vibrational frequency, and interatomic spacing extraordinarily close to experiment, and equally good results have since been found for other properties of molecular hydrogen such as its magnetic and electric susceptibilities. All in all, the description of the hydrogen molecule by quantum mechanics achieves a level of success which makes it one of the most compelling pieces of evidence for the theory itself. The remaining major issue is the interpretation of the exchange integrals. Heisenberg had originally illustrated the idea of a quantum mechanical system oscillating between two states by analogy with classical resonance phenomena, for example, the periodic interchange of energy between two tuning forks on a common base. Quantum mechanical resonance, however, differs from its classical analogues by lowering the total energy of the system. Since a reduced energy implies an attraction, contributions to the interaction arising from the use of wave functions like (2) are often spoken of as exchange forces, pictured as the result of a frequent switching of positions of the two electrons in the molecule—a quite unnecessary piece of mystification. All the forces binding the molecule together are electrical in origin: the exchange integral is merely one of a number of contributions to the electromagnetic energy, and there is moreover no intrinsic need to divide the energy in this particular way. Shortly after the Heitler-London paper, another, very different treatment of molecular structures, the molecular-orbital method, was developed by E. U. Condon, F. Hund, R. S. Mulliken and others, which builds up the solution by modifying the wave function for the helium ion rather than those for two hydrogen atoms. It gives results of comparable accuracy without exchange terms, using instead a quite different pair of resonant structures to find the wave function for the ion. A third mode of division appears in James arid Coolidge’s general variational solution. With these qualifications it must be added that the idea of treating complex molecules as resonating between a number of simple structures, which grew out of the work of Heitler and London their contemporaries, has been amazingly fruitful, London later used to recall Schrodinger’s comment that while he had a high opinion of his equation, expecting it to describe the entire field of chemistry as well as physics was more even than he would have dared.2

London continued for several years to work on molecular theory. In 1928 he formulated a description of chemical reactions as activation processes, and in 1930 with R, Eisenschitz he turned his attention to the quantum theory of intermolecular forces. The modern burgeoning of this branch of physics dates effectively from 1875, when van der Weal applied corrections to the ideal gas equation to describe the phenomena of critical points and the condensation of liquids and showed that the additional terms could be attributed to the combination of a long-range attraction and a shorter-range repulsion between molecules. These must, of course, be distinguished from the more powerful chemical forces. Analysis of their effects gradually advanced during the next forty years, and by 1926, largely through the work of J. E. Lennard-Jones on crystal structures and the transport properties of gases, some knowledge had been gained of their magnitude and distance dependence. Meanwhile, P. J. W. Debye and also W. Keesom in 1921 had given elementary calculations of forces due to the electric dipole moments of molecules and had found an attraction varying inversely as the seventh power of the distance. This attraction, however, was far too weak to account for the observed phenomena. Following two false starts by Born and Heisenberg, the corresponding quantum mechanical calculation given in 1927 with numerical errors by Wang was then corrected and extended by Eisensehitz and London in their paper. They found that fluctuation processes cause a dipole-dipole interaction much greater than De bye’s, because in effect the orbital motions of the electrons in one molecule create large time-varying fields at the other, and the force is proportional not to the mean but to the mean-square value of the field. Such forces are customarily called dispersion forces because they are determined mainly by the outer electrons, which are also responsible for the dispersion of light. The interaction energy is

where e is the electron charge and a0 the Bohr radius the atom. This was the form finally adopted by Lennard-Jones for the attractive part of his potential: it leads to forces varying inversely as the seventh power of the distance. Eisensehitz and London were able to correlate the forces with molecular polarizabilities, and they were later applied to many other matters. More elaborate analyses yielded higher-order corrections. For polar molecules there are additional terms of comparable size, which also obey the inverse-seventh-power law but vary with temperature. A further correction was given in 1946 by H. B. G. Casimir and D. Polder, who discovered that at short distances the retardation of the field introduces phase shifts in the motions of the electrons which make the forces vary more nearly as the inverse eighth power. Effects of this kind are observed in surface phenomena, such as the equilibrium thickness of very thin helium films.

Toward the end of 1932 London completed the manuscript of a book on molecular theory. His agreement for its publication was broken by Springer, the German publisher, after his departure from the country. In England he attempted to arrange a translation, but although several persons offered to he was unable to strike a working relationship any of them. At the time of his death he was planning to rework and translate the material himself. The manuscript is preserved at Duke University Library. London’s departure from Germany coincided with a general shift in his scientific interest. Only on one problem in molecular physics, the diamagnetism of the aromatic compounds, did he spend much time thereafter. While studying the benzene ring in 1937 he began to form the ideas about long-range order that became central in his work on superconductivity.2.

In 1932 London’s brother, Heinz, started a Ph.D. thesis on superconductivity in the low-temperature group at Breslau directed by F. E. Simon. Since Kammerlingh Onnes’ discovery in 1911 that the electrical resistance of mercury vanishes at very low temperatures, the behavior of superconductors with direct currents had been extensively studied, but nothing was known of the effects of high-frequency alternating currents. Following a suggestion by W. Schottky of Siemens, H. London looked for high-frequency losses in superconductors by attempting to detect the Joule heating caused by currents from a 40 M Hz radio source. His search did not lead to anything for several years, but early on he formed some strikingly original ideas about the super conducting state, He decided that a.c. effects, if they exist, probably occur through the existence of two groups of electrons, one subject to losses, the other not. Direct currents then flow only in the super conducting electrons; alternating currents couple inductively to both groups in parallel and so cause dissipation. The same two-fluid model was independently advanced by C. J. Porter and H. B. G. Casimir in 1934 to account for certain thermodynamic properties of superconductors, and since Heinz London gave the idea only in his thesis, it is commonly associated with their names. He then wrote an acceleration equation for the super conducting electrons,

where E is the internal field, J the current, and Λ a constant equal to m/ne2, where m and e are the mass and charge of the electrons and n their number density. The constant Λ, known as the London order parameter, is often attributed to Fritz London but is in fact exclusively due to his brother. Combining (5) with Maxwell’s electromagnetic equations, H. London then concluded that the currents in any superconductor are confined to a shallow surface layer characterized by a penetration depth . This idea is evidently analogous in some degree to the well-known a.c. penetration depth derived by Maxwell for alternating currents in normal metals. The quantity λ was the first of a number of characteristic distances important in the theory of superconductivity. Again it was due exclusively to Heinz London. Similar ideas about the acceleration equation and penetration depth were developed independently by R. Becker, G. Heller, and F. Saunter in an interesting paper which also evaluated magnetic effects in a rotating super conductor.

In 1933 shortly before Heinz London joined his brother at Oxford, W. Meissner and R. Ochsenfeld made a startling discovery. It was well known that currents in superconductors flow in such a way as to shield points inside the material from changes in the external magnetic field. This indeed is an obvious property of any resistance less medium, fully discussed by Maxwell in 1873 long before the discovery of superconductivity.3 But a superconductor does more. Whereas a zero resistance medium only counteracts changes in the field, it actually tends to expel the field present in its interior before cooling. The distinction between the two cases is illustrated in Figure 2. The London quickly saw its implications and in 1935 published a joint paper on the electrodynamics of superconductors, in which they replaced (5) by a new phenomenological equation connecting the current with the magnetic rather than the electric field,

Formally,(6) is nothing other than the integral of the equation obtained by inserting (5)into Maxwell’s equation, curl E =-(1/c)H, and taking the constant of integration as zero. However, in contrast to many physical processes where constants of integration are

trivial, this choice has profound significance: it represents a preferred magnetic state of the superconductor independent of past history. In the paper the logical relation between the propositions is set forth with Fritz London’s philosophical clarity. As the authors observe, equations5 and 6 stand roughly at the same level of generality; but (6) embraces more in respect to the Meissner effect, yet less in another respect, since it implies not5 but the weaker condition curl (ΛJ - E)=0 or, after integration

where μ is an arbitrary scalar quantity. The virtue of the new description is that it covers neither more nor less than the known facts. In the remaining sections the Londons went on to determine boundary conditions, examine the covariant properties of the equations, and give detailed solutions for a sphere and a cylindrical wire which again showed that the currents are restricted to a penetration layer d of order

London continued to study superconductivity for many years, along with the parallel phenomena of super fluidity in liquid helium which were discovered soon afterward and on which he wrote an important paper in 1938. He expounded his ideas on both subjects in various articles and in the two-volume Super Fluids (1950–1954). He gradually came to see a deeper meaning to equation (6). In ordinary electrodynamics the canonical momentum of the electron is given by

where mv is the ordinary momentum and eA/c is a kind of effective momentum associated with the magnetic field, A being the vector potential of the field. The electric current is determined by v but the quantity determining the de Broglie wavelength of the electron is p. Writing p, for the average momentum of the superconducting electrons and using Maxwell’s relation B = curl A and the definition of A, London discovered that (6) is equivalent to

In the special case of an ideal solid superconductor the solution of (9) is ps=0, while for a wire of constant cross section fed at its ends by a current from an external source, ps is uniform over the length and breadth of the wire. This last result is of extraordinary interest. It implies that although the superconducting current is concentrated at the surface of the wire, the wave functions of the electrons extend uniformly throughout the material. From this London came to a radically new concept of the nature of the superconducting state. Ordinary substances when cooled to low temperatures lose the kinetic energy of heat and become progressively more ordered in position: they solidify. For particles subject to classical mechanics, that indeed is the only possibility. For quantum mechanical systems, however, the kinetic energy does not quite vanish at the absolute zero; there is a residual zero-point energy because the positions and moment of the particles are subject to Heisenberg’s uncertainty relation ΔxΔp∽h. Hence, London conjectured, there might in some circumstances be an advantage in energy for a collection of particles to condense with respect to momentum rather than position. This would account for the uniformity of ps. throughout the wire and would imply that the current constitutes a macroscopic quantum state, deseribable by a single wave function, like a gigantic molecule. A striking corollary is that the magnetic flux through a superconducting ring should be quantized, since there must be an integral number of waves around the ring.4 This conjectural condition OB the entire current resembles the quantum condition on a single electron in the de Broglie picture of the atom. London’s unit of magnetic flux was hc/e or about 4 x 10-7 gauss cm2. Some years later the existence of flux quantization was demonstrated independently in Germany and the United States,5 but the unit was found to be half London’s value, a result explained in the microscopic theory of superconductivity by the idea that electrons interact in pairs.

London’s concept of long-range order in momentum space transformed the issue of what the theory of superconductivity was about It no longer had to explain vanishing resistance but, rather, why superconducting electrons acquire order of this particular kind. This opened the way of escape from an embarrassing theorem due to F. Bloch,6 who had rigorously established that the lowest energy state of a system of electrons isolated from external magnetic fields is one of no current. Now if superconductivity were merely an absence of resistance, fluctuation effects would inevitably disturb the current and cause it to decay. In London’s viewpoint no such problem arises, because the current is an excited metastable state, with energy barriers that may (as was later shown) be related to the quantized flux condition.7 The goal for a microscopic theory of superconductivity is then to find the mechanism for cooperative behavior of the electrons. This was achieved by H. Fröhlich; J. Bardeen, L. N. Cooper, and J. R. Schrieffer; and N. Bogoliubov8 in the years immediately after London’s death. The crucial idea, due to Cooper, is that pairs of electrons moving in opposite directions with opposite spins become briefly paired through interaction with the ionic lattice of the metal, In the general case the London equations apply only in one particular limit, and the currents are better described by more elaborate phenomenological equations given in 1952 by V. L. Ginzburg and L. D. Landau. Many of the clues to the solution came through interpreting experiments on the microwave properties of superconductors, which followed the work of Heinz London.

London’s volume of superconductivity contained much else of value on the thermodynamics of superconductors, the intermediate state, and other special topics. One interesting result was that a superconductor spinning with angular velocity w should generate a magnetic field HL equal to (2/mc/e)ω gauss, where m and e are the mass and charge of the electron. The corresponding calculations for a zero-resistance medium spun from rest had been given by Becker, Heller, and Sauter, but London predicted the field would also spontaneously appear as the spinning body is cooled through its transition temperature, in analogy with Meissner and Oehsenfeld’s discovery. The effect was demonstrated experimentally in 1960.9 An interesting point, which has been little explored, is that HL appears to depend on the rotation of the superconductor relative to the universe as a whole. There then appears to be some constraint on the underlying quantum condition closely related to that determining rotation in gravitational theory. Besides their theoretical implications, the ideas discussed by London have led to many interesting advances in technology, for example in the application of quantized flux devices to measurement of very low magnetic fields. The authors and their colleagues are planning to use the magnetic moment of a rotating superconductor for readout of a high-precision gyroscope to perform a new test of general relativity in a satellite suggested by L. L Schiff.

In 1908 Kammerlingh Onnes liquefied helium at a temperature of 4.2° K. During the 1920’s evidence began to accumulate that at 2.19°K. the liquid undergoes a peculiar transition, marked by discontinuities in the specific heat and density curves, into another phase which became known as liquid helium II; but not until 1938 were its extraordinary superfluid properties discovered simultaneously by P. Kapitsa and by J. F. Allen and A, P. Keesom. Allen with several colleagues then established that the heat current in the helium II is not linear with temperature and that a pressure gradient proportional to heat input exists in the fluid. The latter effects are often called the fountain pressure, since Allen and J. Jones demonstrated it in an especially striking way by creating a helium fountain, Clearly the mass flow and heat transfer equations of helium II must differ from those of any other fluid; and in addition, the nature of the phase transition—indeed, even the existence of two distinct liquid phases—was puzzling. Thinking over the problem, London was reminded of a strange feature of quantum statistics derived in 1924 by Einstein. In 1923 S. N. Bose had shown that Planck’s well-known radiation formula might be derived from the hypothesis of light quanta (photons), by assuming that the photons are subject to a different kind of statistics from classical Maxwell-Boltzmann particles, with the statistical specification based not on the number of particles but on the number of particle states. Bose communicated his result privately to Einstein, who arranged for its publication and then wrote two papers extending the statistics to other quantum gases. One of Einstein’s conclusions was that at low temperatures such a gas would have more particles than the number of available states and would then undergo a peculiar kind of condensation with the surplus molecules concentrated in the lowest possible quantum state, Applying the new statistics to ordinary molecules, Einstein then argued that the condensation would have perceptible effects in gases at low temperatures; the viscosity of helium gas, for example, might be expected to fall off rapidly below 40° K. All this seemed rather farfetched: it was not obvious that the new statistics applied to gases. Indeed, a year later E. Fermi and P. A. M. Dirac showed that electrons obey another, quite different kind of quantum statistics, and in 1927 G. Uhlenbeck claimed that Einstein had mistakenly approximated a sum by an integral and that in the correct calculation no condensation would occur. There things rested until London revived the argument and made the even more radical suggestion that Bose-Einstein condensation might occur in liquids as well as gases and thus might account for the peculiar behavior of liquid helium II.

London’s suggestion was controversial and also difficult to develop owing to the unsatisfactory state of the theory of liquids. The next advance was due to L. Tisza. Partly through London’s idea and partly through considering the results of experiments with oscillating disks, which unlike those on capillary flow gave a finite viscosity, he suggested that helium II may be conceived of as a mixture of two liquids, superfiuid and normal, analogously with the two-fluid model of superconductivity. In 1939 Heinz London made a further important contribution by proving from thermodynamic arguments that the superfluid does not carry entropy. In this form the two-fluid model provided a framework for many experimental discoveries over a number of years. Meanwhile, a different approach to the fundamental theory was advanced by Landau, and the idea of Bose-Einstein condensation was heavily criticized. However, London stuck to his guns. An important test, as he pointed out, was to search for super fluidity in the rare isotope He3 which, unlike ordinary He4, contains an odd number of particles and may be expected to obey Fermi-Dirac rather than Bose-Einstein statistics. In fact no super-fluidily has been observed in He3 down to 10-2°K. In volume II of Superfluids London gave an approximate treatment of a Bose-Einstein liquid, following E. Guggenheim’s smoothed-potential model of the liquid state, and estimated the condensation temperature at roughly 3.13° K, as compared with the experimental value of 2.19° K, He also continued to emphasize the close analogy between super fluidity and superconductivity. Here he was in more difficulty than he cared to admit. Electrons obey Fermi-Dirac statistics, and there seemed to be no grounds for linking superconductivity with Bose-Einstein condensation. With the emergence of the microscopic theory, however, the tables were turned on London’s critics: paired electrons do behave as Bose particles, and his interpretation of the condensation extends to superconductivity also.

There is a perspective in London’s work that has made many of his ideas become progressively more influential with the passage of time. One of his favorite opinions was that some concept of long-range order would eventually prove important to the understanding of biological systems. Although the suggestion remains in the nascent phase it has already had interesting consequences. W. A. Little has proposed that a particular class of long-chain organic molecules might be expected to have superconductive properties, with transition temperatures around room tern-perature.10 Although organic superconductors have not yet been made, the idea has raised many interesting questions of the kind that would have appealed to London,

NOTES

1. L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics (New York, 1935), p. 340.

2. Personal recollections of conversations between London and W, M. Fairbank.

3. J. C. Maxwell, Treatise on Electricity and Magnetism, II (London, 1873), sees. 654, 655.

4. F. London, in Physical Review,74 (1948), 570, is the earliest statement of flux quantization.

5. B. S. Deaver, Jr. and W. M. Fairbank, in Physical Review Letters, 7 (1961), 43; R. Doll and M. Näbauer, ibid., 1

6. L. Brillouin, in Proceedings of the Royal Society, 75 (1949), 502. crediting theorem to Bloch.

7. N. Bycrs and C. N. Yang, in Physical Review Letters, 7 (J961), 46.

8. H. Fröhlich, in Physical Review, 79 (1950), 845; J. Bardeen, L. N. Cooper, and J. R. SehriefTer, ibid., 106 (1957), 162; 108 (1957), 1175; and R, Bogoliubov, in Zhumal eksperimentalnoi i teoreticheskoi fisiki,34 (1958), 58; translated in Soviet Physics JETP, 7 (1958), 41.

9. A. F. Hildebrandt, in Physical Review letters, 12 (1964), 190; A. King, Jr., J. B. Hendricks, and H. E. Rorschach, Jr., in Proceedings of the Ninth international Conference cm Temperature Physics (New York, 1965), p. 466; M. Bol and W. M. Fairbank, ibid., p. 471.

10. W. A. Little, in Physical Review,134 (1964), 1416,

BIBLIOGRAPHY

I. Original Works. London’s published books are La théorie de observation en mécanique (Paris, 1939), written with E. Bauer (a copy of this rare work is in Brown University Library); Super fluids: Vol. I, Macroscopic Theory of Superconductivity; Vol. II, Macroscopic Theory of Superflaid Helium (New York, 1950–1954); 2nd ed., rev., reprinted in the Dover series with additional material by other authors, 2 vols. (New York, 1961–1964), with bibliography of London’s scientific papers, by Edith London, l, xv-xviii. A large collection of notebooks and MSS is preserved at the Duke University Library, Durham, N. C, together with two bound vols, containing London’s complete published papers. Some MSS of scientific interest remain m Mrs. London’s possession.

II. Secondary Literature. Personal biographical material by E. London and a sketch of London’s scientific work by L. W. Nordheim are in Superfluids, 2nd ed., I, v-xviii.

On the chemical bond the monographs by L. Pauling, Nature of the Chemical Bond, 3rded. (Ithaca, N. Y., 1960); and C. A, Coulson, Valence (Oxford, 1960), are useful. On dispersion forces, see S. G. Brush, “Interatomic Forces and Gas Theory From Newton to Lennard-Jones,” in Archives of Rational Mechanics and Analysis,39, no, 1 (1970), 1–29.

On superconductivity, see D. Shoenberg, Superconductivity (Cambridge, 1950); J. Bardeen and J. R. Schrieffer, in C. J. Gorter, ed., Progress in Low Temperature Physics, III (Amsterdam, 1961), 170–287; and P. de Gennes, Super-conductivity of Metals and Alloys (New York, 1966). On superfluidity, see K. R. Atkins, Liquid Helium (Cambridge, 1958); and J. Wilks, Properties of Liquid and Solid Helium (Oxford, 1967),

C. W. F. Everitt

W. M. Fairbank

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