John C. Slater Explained

John C. Slater
Birth Date:22 December 1900
Birth Name:John Clarke Slater
Birth Place:Oak Park, Illinois, U.S.
Death Place:Sanibel Island, Florida, U.S.
Field:Physics
Alma Mater:
    Work Institution:
    Known For:
    Awards:
      Doctoral Advisor:Percy Williams Bridgman
      Doctoral Students:
      Thesis Title:The Compressibility of the Alkali-Halides
      Thesis Year:1923

      John Clarke Slater (December 22, 1900 – July 25, 1976) was an American physicist who advanced the theory of the electronic structure of atoms, molecules and solids.[1] [2] He also made major contributions to microwave electronics. He received a B.S. in physics from the University of Rochester in 1920 and a Ph.D. in physics from Harvard in 1923, then did post-doctoral work at the universities of Cambridge (briefly) and Copenhagen. On his return to the U.S. he joined the physics department at Harvard.

      In 1930, Karl Compton, the president of MIT, appointed Slater as chairman of MIT's department of physics. He recast the undergraduate physics curriculum, wrote 14 books between 1933 and 1968, and built a department of international prestige. During World War II, his work on microwave transmission, done partly at the Bell Laboratories and in association with the MIT Radiation Laboratory, was significant in the development of radar.

      In 1950, Slater founded the Solid State and Molecular Theory Group (SSMTG) within the physics department. The following year, he resigned the chairmanship of the department and spent a year at the Brookhaven National Laboratory of the Atomic Energy Commission. He was appointed Institute Professor of Physics and continued to direct work in the SSMTG until he retired from MIT in 1965, at the mandatory retirement age of 65.

      He then joined the Quantum Theory Project of the University of Florida as research professor, where the retirement age allowed him to work for another five years. The SSMTG has been regarded as the precursor of the MIT Center for Materials Science and Engineering (CMSE).[3] His scientific autobiography[4] and three interviews[5] [6] present his views on research, education and the role of science in society.

      Slater was nominated for the Nobel Prize, in both physics and chemistry, multiple times,[7] and he received the National Medal of Science in 1970. In 1964, Slater and his then-92-year-old father, who had headed the Department of English at the University of Rochester many years earlier, were awarded honorary degrees by that university. Slater's name is part of the terms Bohr-Kramers-Slater theory, Slater determinant and Slater orbital.

      Early life and education

      Slater's father, born in Virginia, who had been an undergraduate at Harvard, became head of the English Department at the University of Rochester, which would also be Slater's undergraduate alma mater. Slater's youthful interests were with things mechanical, chemical, and electrical. When Slater entered the University of Rochester in 1917 he took physics courses and as a senior assisted in the physics laboratory and did his first independent research for a special honors thesis, a measurement of the dependence on pressure of the intensities of the Balmer lines of hydrogen.

      He was accepted into Harvard graduate school, with the choice of a fellowship or assistantship. He chose the assistantship, during which he worked for Percy W. Bridgman. He followed Bridgman's courses in fundamental physics and was introduced into the then-new quantum physics with the courses of E. C. Kemble. He completed the work for the Ph.D. in three years by publishing his (1924) paper Compressibility of the Alkali Halides, which embodied the thesis work he had done under Bridgman. His heart was in theory, and his first publication was not his doctor's thesis, but a note (1924) to Nature on Radiation and Atoms.[8]

      After receiving his Ph.D., Slater held a Hamard Sheldon Fellowship for study in Europe. He spent a period in Cambridge, England, before going to Copenhagen. He did not have a happy time working with Bohr who he found domineering and regretted that his name was attached to the ill-fated Bohr-Kramers-Slater (BKS) theory. Slater already had the idea that it was the photon that carried radiation energy. As he relates:

      On the plus side, Slater's name was now well known by association with Bohr. On returning to America, Slater joined the Harvard Physics Department.

      Professional career

      Chairing the Department of Physics at MIT

      When he became president of MIT, Karl Compton "courted" Slater to chair the physics department.[9] "Administration (of the Department) took up a good deal of time, more time than he (Slater) would have preferred. John was a good chairman." The following items from the successive issues of the annual MIT President's Report[10] trace the growth and visibility of the Department under Slater's leadership, before World War II, and the ability of the department to contribute to defense during the war. The first two quotations are from chapters written by Compton in the successive reports. The other quotations come from the sections about the department, that Slater wrote. These include statements affecting policies in physics education and research at large, and show his deep commitment to both.

      Setting up interdepartmental laboratories, by restructuring existing laboratories using, as a model, the conversion of the Radiation Laboratory into the Research Laboratory of Electronics (RLE) by Julius Stratton and Albert Hill.

      Financing student assistantships and helping shape the role of government financing on an unprecedented scale.

      Overseeing Robley Evans' Radioactivity Center (containing a cyclotron) and Van de Graaff's High Voltage Laboratory.

      Recruiting physicists familiar with the Manhattan project to build the Laboratory for Nuclear Science and Engineering.[15] This was directed by Jerrold Zacharias. Its first members included Bruno Rossi and Victor Weisskopf.

      Setting up the Acoustics Laboratory, directed by Richard Bolt, and the Spectroscopy Laboratory directed by the chemist Richard Lord.

      Throughout his Chairmanship, Slater taught, wrote books, produced ideas of major scientific importance, and interacted with colleagues throughout the local, national and international scientific communities. At the personal level, Morse states: "Through most of (the 1930s) he looked more like an undergraduate than a department head ... he could render his guests weak with laughter simply by counting ... in Danish." Much later, S.B. Trickey wrote "While I got to know him reasonably well, I was never able to call J.C. Slater by his given name. His seeming aloofness turned out more to be shyness."[17]

      Research

      Atoms, molecules and solids: research preceding World War II

      Returning in time to 1920, Slater had gone to Harvard to work for a Ph.D. with Percy Bridgman, who studied the behaviour of substances under very high pressures. Slater measured the compressibility of common salt and ten other alkali halides—compounds of lithium, sodium, potassium and rubidium, with fluorine, chlorine and bromine. He described the results as "exactly in accord with Bohr's recent views of the relation between electron structure and the periodic table". This brought Slater's observation concerning the mechanical properties of ionic crystals into line with the theory that Bohr had based on the spectroscopy of gaseous elements. He wrote the alkali halide paper in 1923, having "by the summer of 1922" been "thoroughly indoctrinated ... with quantum theory", in part by the courses of Edwin Kemble following a fascination with Bohr's work during his undergraduate days.[18] In 1924, Slater went to Europe on a Harvard Sheldon Fellowship.[19] After a brief stay at the University of Cambridge, he went on to the University of Copenhagen, where "he explained to Bohr and Kramers his idea (that was) a sort of forerunner of the duality principle, (hence) the celebrated paper" on the work that others dubbed the Bohr-Kramers-Slater (BKS) theory. "Slater suddenly became an internationally known name.". Interest in this "old-quantum-theory" paper subsided with the arrival of full quantum mechanics, but Philp M. Morse's biography states that "in recent years it has been recognized that the correct ideas in the article are those of Slater." Slater discusses his early life through the trip to Europe in a transcribed interview.

      Slater joined the Harvard faculty on his return from Europe in 1925, then moved to MIT in 1930. His research papers covered many topics. A year by year selection, up to his switch to work relating to radar includes:

      In his memoir, Morse wrote "In addition to other notable papers ... on ... Hartree's self-consistent field, the quantum mechanical derivation of the Rydberg constant, and the best values of atomic shielding constants, he wrote a seminal paper on directing valency " (what became known, later, as linear combination of atomic orbitals).In further comments, John Van Vleck pays particular attention to (1) the 1925 study of the spectra of hydrogen and ionized helium, that J.V.V. considers one sentence short of proposing electron spin (which would have led to sharing a Nobel prize), and (2) what J.V.V. regards as Slater's greatest paper, that introduced the mathematical object now called the Slater determinant. "These were some of the achievements (that led to his) election to the National Academy ... at ... thirty-one. He played a key role in lifting American theoretical physics to high international standing." Slater's doctoral students, during this time, included Nathan Rosen Ph.D. in 1932 for a theoretical study of the hydrogen molecule, and William Shockley Ph.D. 1936 for an energy band structure of sodium chloride, who later received a Nobel Prize for the discovery of the transistor.

      Research during the war and the return to peace time activities

      Slater, in his experimental and theoretical work on the magnetron (key elements paralleled his prior work with self-consistent fields for atoms) and on other topics at the Radiation Laboratory and at the Bell Laboratories did "more than any other person to provide the understanding requisite to progress in the microwave field", in the words of Mervin Kelley, then head of Bell Labs, quoted by Morse.

      Slater' publications during the war and the post-war recovery include a book and papers on microwave transmission and microwave electronics,[46] [47] linear accelerators,[48] cryogenics,[49] and, with Francis Bitter and several other colleagues, superconductors,[50] These publications credit the many other scientists, mathematicians and engineers who participated. Among these,George H. Vineyard received his Ph.D. with Slater in 1943 for a study of space charge in the cavity magnetron. Later, he became director of the Brookhaven National Laboratory and President of the American Physical Society.[51] The work of the Radiation Laboratory paralleled research at the Telecommunications Research Establishment in England and the groups maintained a productive liaison.

      The Solid State and Molecular Theory Group

      Activities

      In the words of Robert Nesbet: "Slater founded the SSMTG with the idea of bringing together a younger generation of students and PostDocs with a common interest in the electronic structure and properties of atoms, molecules and solids. This was in part to serve as a balance for electronic physics to survive the overwhelming growth of nuclear physics following the war" .[52]

      George F. Koster soon completed his Ph.D., joined the faculty, and became the senior member of the group. He wrote "During the fifteen-year life of the group some sixty persons were members and thirty-four took doctoral degrees with theses connected with its work. In my report I have been unable to separate the work of Slater from that of the group as a whole. He was part of every aspect of the group's research efforts."[53]

      Nesbet continued "Every morning in SSMTG began with a coffee session, chaired by Professor Slater, with the junior members seated around a long table ... Every member of the group was expected to contribute a summary of his own work and ideas to the Quarterly Progress Report". The SMMTG QPRs had a wide distribution to university and industrial research libraries, and to individual laboratories. They were quoted widely for scientific and biographical content, in journal articles and government reports and libraries are starting to put them online.[54]

      To begin the work of the group, Slater "distilled his experience with the Hartree self-consistent field method" into (1) a simplification that became known as the Xα method,[55] and (2) a relationship between a feature of this method and a magnetic property of the system.[56] These required computations that were excessive for "pencil and paper" work. Slater was quick to avail the SSMTG of the electronic computers that were being developed. An early paper on augmented plane waves[57] used an IBM card programmed calculator. The Whirlwind was used heavily, then the IBM 704 in the MIT Computation Center and then the IBM 709 in the Cooperative Computing Laboratory (see below).

      Solid state work progressed more rapidly at first in the SSMTG, with contributions over the first few years by George F. Koster, John Wood, Arthur Freeman and Leonard Mattheis. Molecular and atomic calculations also flourished in the hands of Fernando J. Corbató, Lee Allen and Alvin Meckler. This initial work followed lines largely set by Slater. Michael Barnett came in 1958. He and John Wood were given faculty appointments. Robert Nesbet, Brian Sutcliffe, Malcolm Harrison and Levente Szasz brought in a variety of further approaches to molecular and atomic problems. Jens Dahl, Alfred Switendick, Jules Moskowitz, Donald Merrifield and Russell Pitzer did further work on molecules, and Fred Quelle on solids.

      Slater rarely included his name on the papers of SSMTG members who worked with him. Major pieces of work which he did coauthor dealt with applications of (1) group theory in band structure calculations[58] and (2) equivalent features of linear combination of atomic orbital (LCAO), tight binding and Bloch electron approximations, to interpolate results for the energy levels of solids, obtained by more accurate methods,[59]

      People

      A partial list of members of the SSMTG (Ph.D. students, post-doctoral members, research staff and faculty, in some cases successively, labeled †, ‡, ৳, ¶), together with references that report their SSMTG and later activities, follows.

      Distinguished visitors included Frank Boys, Alex Dalgarno, Ugo Fano, Anders Fröman, Inga Fischer-Hjalmars, Douglas Hartree, Werner Heisenberg, Per-Olov Löwdin, Chaim Pekeris, Ivar Waller and Peter Wohlfarth.

      Slater's further activities at MIT during this time

      In the 1962 President's Report, Jay Stratton wrote (on p. 17) "A faculty committee under the chairmanship of Professor John C. Slater has taken primary responsibility for planning the facilities in the new Center for Materials. These include a new Cooperative Computing Laboratory completed this year and equipped with an I.B.M. 709 Computer".

      The name Center for Materials Science and Engineering (CMSE) was adopted soon afterward. It embodied the ethos of interdepartmental research and teaching that Slater had espoused throughout his career. The first director was R.A. Smith, previously head of the physics division of the Royal Radar Establishment in England. He, Slater and Charles Townes, the provost, had been in close acquaintance since the early years of World War II, working on overlapping topics.[80]

      The center was set up, in accordance with Slater's plans. It "supported research and teaching in Metallurgy and Materials Science, Electrical Engineering, Physics, Chemistry and Chemical Engineering", and preserved MIT as a focus for work in solid state physics. By 1967, two years after Slater left, the MIT Physics Department "had a very, very small commitment to condensed matter physics" because it was so "heavily into high energy physics."[81] But in the same year, the CMSE staff included 55 professors and 179 graduate students. The Center continues to flourish in the 21st century.

      The Cooperative Computing Laboratory (CCL) was used, in its first year by some 400 faculty, students and staff. These included (1) members of the SSMTG and the CCL running quantum mechanical calculations and non-numeric applications[82] directed by Slater, Koster, Wood and Barnett, (2) the computer-aided design team of Ross, Coons and Mann, (3) members of the Laboratory for Nuclear Science, (4) Charney and Phillips in theoretical meteorology, and (5) Simpson and Madden in geophysics (from 1964 President's report, p. 336-337).

      Personal life and death

      In 1926, he had married Helen Frankenfeld. Their three children (Louise Chapin, John Frederick, and Clarke Rothwell) all followed academic careers. Slater was divorced and in 1954 he married Rose Mooney, a physicist and crystallographer, who moved to Florida with him in 1965.[8]

      At the University of Florida (Gainesville) where the retirement age was 70, Slater was able to enjoy another five years of active research and publication as a research professor in the Quantum Theory Project (QTP). In 1975, in his scientific autobiography, he wrote: "The Florida Physics Department was a congenial one, with main emphasis on solid state physics, statistical physics and related fields. It reminded me of the MIT department in the days when I had been department head there. It was a far cry from the MIT Physics Department which I was leaving; by then it had been literally captured by the nuclear theorists."[4] Slater published to the end of his life: his final journal paper, published with John Connolly in 1976, was on a novel approach to molecular orbital theory.[83]

      Slater died in Sanibel Island, Florida in 1976.

      As an educator and advisor

      Slater's concern for others is illustrated by a dialog that Richard Feynman relates. It took place at the end of Feynman's undergraduate days at MIT, when he wanted to stay on to do a Ph.D.[84] "When I went to Professor Slater and told him of my intentions he said: 'We will not have you here'. I said 'What?' Slater said 'Why do you think you should go to graduate school at MIT?' 'Because it is the best school for science in the country' ... 'That is why you should go to some other school. You should find out how the rest of the world is.' So I went to Princeton. ... Slater was right. And I often advise my students the same way. Learn what the rest of the world is like. The variety is worthwhile."

      Summary

      From the memoir by Philip Morse: "He contributed significantly to the start of the quantum revolution in physics; he was one of the very few American-trained physicists to do so. He was exceptional in that he persisted in exploring atomic, molecular and solid state physics, while many of his peers were coerced by war, or tempted by novelty, to divert to nuclear mysteries."

      To paraphrase John Connolly,[85] it can be said that the contributions of John C. Slater and his students in the SSMTG and the Quantum Theory Project laid the foundations of the density functional theory approximation in quantum theory.

      Slater's papers were bequeathed to the American Philosophical Society by his widow, Rose Mooney Slater, in 1980 and 1982.[86] In August 2003, Alfred Switendick donated a collection of Quarterly Reports of the MIT Solid State and Molecular Theory Group (SSMTG), dating from 1951 to 1965.

      Awards and honors

      Books

      External links

      Notes and References

      1. Per-Olav Lowdin (ed.) Quantum Theory of Atoms, Molecules and the Solid State, A Tribute to John C. Slater, Academic Press, N.Y. 1966.
      2. Van Vleck, John H.. John Hasbrouck Van Vleck. John C. Slater. Physics Today. October 1976. 29. 10. 68–69. 10.1063/1.3024428. 1976PhT....29j..68V. dead. https://web.archive.org/web/20130927202403/http://www.physicstoday.org/resource/1/phtoad/v29/i10/p68_s1?bypassSSO=1. 2013-09-27.
      3. Web site: MIT Center for Materials Science and Engineering . Mit.edu . 2011-03-10 . 2011-03-14.
      4. Book: Slater, J. C.. Solid-State and Molecular Theory: A Scientific Biography. New York. Wiley. 1975. 978-0-471-79681-7.
      5. Web site: Oral history interview transcript with John C. Slater 3 October 1963, American Institute of Physics, Niels Bohr Library & Archives . . 2011-03-14 . 2011-06-04 . https://web.archive.org/web/20110604132639/http://www.aip.org/history/ohilist/4892_1.html . dead .
      6. http://www.aip.org/history/ohilist/4893_1.html Oral History Transcript - Dr. John C. Slater, interviewed by Charles Weiner, Niels Bohr Center and Archives for the History of Physics. Session I, Gainesville, February 23, 1970.
      7. Web site: 2020-04-01 . John Clarks Slater . 2022-04-05 . NobelPrize.org . en-US.
      8. Web site: Biographical Memoirs Home . Nap.edu . 2015-12-24.
      9. Web site: The History of the MIT Department of Physics, MIT Department of Physics web site . Web.mit.edu . 2003-05-23 . 2011-03-14.
      10. http://libraries.mit.edu/archives/mithistory/presidents-reports/1930.pdf President's Report, Massachusetts Institute of Technology Bulletin, volume 622, number 1, 1930
      11. Program for Dedication of George Eastman Research Laboratories. Chem. Eng. News. 1933. 11. 8. 130. 10.1021/cen-v011n008.p130 . 31 January 2024 .
      12. Web site: , Prof. Robley D. Evans of MIT Dies at 88, MIT News, Jan, 24, 1996 . Mit.edu . 1996-01-04 . 2011-03-14.
      13. https://www.ams.org/meetings/lectures/meet-gibbs-lect Josiah Willard Gibbs Lectures
      14. Slater, J. C.. Physics and the wave equation (Part 1). Bull. Amer. Math. Soc.. 1946 . 52. 5. 392–400. 0015639. 10.1090/s0002-9904-1946-08558-4. free.
      15. Web site: MIT Laboratory for Nuclear Science . Web.mit.edu . 2011-03-14.
      16. Web site: AP . Nathaniel H. Frank, 80, Dies; Led Physics Dept. At M.I.T., New York Times, Feb. 25, 1984 . . 1984-02-25 . 2011-03-14.
      17. http://pdfserve.informaworld.com/467823_751318052_930068296.pdfS.B. Trickey, Of science and scientists in QTP, Molecular Physics, 108 (21-23) 2841-2845, 2010.
      18. J.H. Van Vleck, Remarks, Slater Memorial Session, American Physical Society, Chicago, 7 February 1977, quoted in Morse's Biographical Memoir.
      19. Web site: Harvard University Committee on General Scholarships | Traveling Fellowships . Scholarship.harvard.edu . 2015-12-24 . 2015-11-23 . https://web.archive.org/web/20151123014236/http://www.scholarship.harvard.edu/dissertation.html . dead .
      20. J.C. Slater, Compressibility of the alkali halides, Physical Review, 23, 488-500, 1924.
      21. N. Bohr, H.A. Kramers and J.C. Slater, The quantum theory of radiation, Philosophical Magazine, 47, 785-802, 1924.
      22. J.C. Slater and G.R. Harrison, Line breadths and absorption probabilities in sodium vapor, Physical Review, 26, 419-430, 1925.
      23. J.C. Slater, Interpretation of the hydrogen and helium spectra, Proceedings of the National Academy, 11, 732-738, 1925.
      24. J.C. Slater, Spinning electrons and the structure of spectra, Nature, 117, 278, 1926.
      25. J.C. Slater, Radiation and absorption on Schrödinger's theory, Proceedings of the National Academy of Sciences, 13, 7-12, 1927.
      26. J.C. Slater, The self-consistent field and the structure of atoms, Physical Review, 32, 339-348, 1928;
      27. J.C. Slater Central fields and the Rydberg formula in wave mechaincs, Physical Review, 31, 333-343, 1928.
      28. J.C. Slater, The theory of complex spectra, Physical Review, 34, 1293-1323, 1929.
      29. J.C. Slater, Atomic shielding constants, Physical Review, 36, 57-64, 1930.
      30. J.C. Slater, Directed valence in polyatomic molecules, Physical Review, 37, 481-489, 1931.
      31. J.C. Slater and J.G. Kirkwood, Van der Waals forces in gases, Physical Review, 38, 237-242, 1931.
      32. J.C. Slater, Analytic atomic wave functions, Physical Review, 42, 33-43, 1932.
      33. J.C. Slater, The electron theory of metallic conduction, Science, 77, 595-597, 1933.
      34. J.C. Slater, The electronic structure of metals, Reviews of Modern Physics, 6, 209-280, 1934.
      35. J.C. Slater and H.M. Krutter, Physical Review, 47, 559-568.
      36. J.C. Slater, The ferromagnetism of Ni, Physical Review, 49, 537-545, 1936.
      37. E. Rudberg and J.C. Slater, Theory of inelastic scattering from solids, Physical Review, 50, 150-158, 1936.
      38. J.C. Slater and W. Shockley, Optical absorption by the alkali halides, Physical Review, 50, 705-719, 1936.
      39. J.C. Slater, Wave functions in a periodic potential, Physical Review, 51, 846-851, 1937.
      40. J.C. Slater, The nature of the superconducting state, Physical Review, 51, 195-202 and 52, 214-222, 1937.
      41. J.C. Slater, Theory of ferromagnetism, lowest energy levels, Physical Review, 52, 198-214, 1937.
      42. J.C. Slater, Electrodynamics of ponderable bodies, Journal of the Franklin Institute, 225, 277-287, 1938.
      43. J.C. Slater, Note on Gruneisen's constant for the incompressible metals, Physical Review, 57, 744-746, 1940.
      44. J.C. Slater, Note on the effect of pressure on the Curie point of iron-nickel alloys, Physical Review, 58, 54-56, 1940.
      45. https://aip.scitation.org/doi/10.1063/1.1750821 J.C. Slater, Theory of the transition in . Journal of Chemical Physics, 9, 16-33, 1941.
      46. J.C. Slater, Microwave transmission, McGraw-Hill, New York, 1942; reissued Dover Publications, New York, 1959
      47. J.C. Slater, Microwave electronics, Reviews of Modern Physics, 18, 441-512, 1946; Microwave electronics, Van Nostrand, Princeton, 1950.
      48. J.C. Slater, The design of linear accelerators, Reviews of Modern Physics, 20, 473-518, 1948.
      49. J.C. Slater, The MIT International Conference on the Physics of Very Low Temperatures, Science, 100, 465-467, 1949.
      50. J.C. Slater, F. Bitter, J.B. Garrison, J. Halpern, E. Maxwell and C.F. Squire, Superconductivity of lead at 3 cm. wave length, Physical Review, 70, 97-98. 1946; J.C. Slater, E. Maxwell and P.M. Marcus, Surface impedance of normal and superconductors at 24,000 megacycles per second, Physical Review, 76, 1331-1347, 1949.
      51. Martin Blume, Maurice Goldhaber and Nicholos P. Samios . George H. Vineyard . . 40 . 10 . 146 . 1987 . 10.1063/1.2820246 . 1987PhT....40j.146B . free .
      52. R.K. Nesbet, John C. Slater and the SSMTG in 1954-1956, Molecular Physics, 108 (21-23) 2867-2869, 2010.
      53. G. Koster, remarks, Slater Memorial Session, American Physical Society, Chicago, 7 February 1977.
      54. (i) 10.1016/0921-4526(91)90423-C . D. D. Koellig . F-Electron systems: pushing band theory . . 172 . 1–2 . 117–123 . 1991. 1991PhyB..172..117K ., quotes Slater's biographical comments in QPR 61, 1956 about A. J.Freeman; (ii) . 139 . 4 . A1333–A1337 . T.L. Loucks . Relativistic electronic structure in crystals. I. Theory] . 1965 . 10.1103/PhysRev.139.A1333 . 1965PhRv..139.1333L., refers to P.M. Scop, QPR 54, 1964; (iii) Brown. Robert G.. Ciftan. Mikael. A generalized non-muffin-tin theory of band structure. International Journal of Quantum Chemistry. 26. 87–104. 1984. 10.1002/qua.560260813. 94230818 . refers to J.F. Kenney, QPR 53, 38, 1964; (iv) Yasui . Masaru . Hayashi . Eisuke . Shimizu . Masao . Self-Consistent Band Calculations for Iron in Paramagnetic and Ferromagnetic States . Journal of the Physical Society of Japan . 34 . 2 . 396–403 . 1973 . 10.1143/JPSJ.34.396. 1973JPSJ...34..396Y . refers to R.E. Watson, QPR 12, 1959; (v) consists of QPR 49, 1963, put online by the Defence Technical Information Center.
      55. J. C. Slater, A simplification of the Hartree–Fock method, Physical Review, 81, 385-390, 1951.
      56. J. C. Slater, Magnetic effects and the Hartree–Fock equation, Physical Review, 82, 538-541, 1951.
      57. Wood . J. . Pratt . G. . Wave Functions and Energy Levels for Fe as Found by the Unrestricted Hartree-Fock Method . Physical Review . 107 . 4 . 995–1001 . 1957 . 10.1103/PhysRev.107.995. 1957PhRv..107..995W .
      58. Physical Review. 126. 4. 1307. 10.1103/PhysRev.126.1307 . J.C. Slater, G.F. Koster and J.H. Wood . Symmetry and free electron properties of Gallium energy bands . 1962. 1962PhRv..126.1307S .
      59. 10.1103/PhysRev.94.1498 . J. C. Slater and G. F. Koster . Simplified LCAO Method for the Periodic Potential Problem . . 94 . 6 . 1498–1524 . 1954. 1954PhRv...94.1498S .
      60. Michael P. Barnett and James Harrison, eds. Tribute to Leland C. Allen, International Journal of Quantum Chemistry, 95 (6) 659-889, 2003.
      61. Louis Burnelle and Marie J. Kranepool, On σ → π* transitions in aromatic hydrocarbons, Journal of Molecular Spectroscopy, 37 (3) 383-393, 1971.
      62. https://www.researchgate.net/publication/251552820_Polymerization_dependence_of_the_entropy_of_homo-oligomer_peptides B. Viskolcz, I.G. Csizmadia, S.J.K. Jensen, A. Perczel Polymerization dependence of the entropy of homo-oligomer peptides, Chemical Physics Letters, 501 (1-3) 30-32, 2010
      63. J. P. Dahl, Introduction to the quantum world of atoms and molecules, World Scientific, 2001.
      64. Web site: Northwestern University, Donald Ellis materials group web site . Appliedphysics.northwestern.edu . 2010-10-05 . 2011-03-14 . 2013-05-20 . https://web.archive.org/web/20130520194944/http://www.appliedphysics.northwestern.edu/faculty/don-ellis.html . dead .
      65. http://www.matsci.northwestern.edu/faculty/ajf.html Arthur J. Freeman
      66. Web site: Bob Futrelle's home page . Ccs.neu.edu . 2010-01-10 . 2011-03-14.
      67. Flux Quantization without Off-Diagonal Long Range Order in a Thin Hollow Cylinder (with Y. Imry), Sol. State Comm. 7, l39l (1969); Quantum Tunneling of Magnetization in Small Ferromagnetic Particles, (with E.M. Chudnovsky), Phys. Rev. Lett. 60, 661 (1988); Bloch and Josephson Oscillations in a Ring of an Ideal Bose Gas - Proceedings of the Conference on Perspectives of Mesoscopic Physics, Weizmann Institute, 2009; The Physics of Music and Color, published in September, 2011 by Springer Publishers, N.Y.,
      68. http://cs.nyu.edu/web/People/inmemoriam.html New York University, Department of Computer Science, in memoriam web site
      69. F. Herman, Theoretical Investigation of the Electronic Energy Band Structure of Solids, Reviews of Modern Physics 30, 102–121, 1958; Frank Herman, International Symposium on Computational Solid State Physics Wildbad (Germany), Plenum, 1972 .
      70. http://www.digital60.org/about/biographies/others/ David Howarth, Operating Systems Mark 1 to Atlas
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      72. (i) G.F. Koster, R.G. Wheeler, J.O. Dimmock, and H. Statz, The Properties of the Thirty-Two Point Groups, MIT Press, 1965, . (ii) G.F. Koster and C.W. Nielson, Spectroscopic Coefficients for the pn, dn, and fn,MIT Press,
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      92. From the Preface (p. v): "The present book is the second of several volumes which are intended to replace the Introduction to Theoretical Physics written by the same authors in 1933. By separating the material on mechanics, on electromagnetism, and on the quantum theory, we believe that it is possible to give a somewhat better rounded treatment of each of these fields."

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