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Wave Mechanics

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Arnold Sommerfeld
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Abstract

In retrospect it seems as though following World War I quantum physics intensified critically and in a revolutionary act in the mid 1920s freed itself from the many contradictions of the old quantum theory. The breakthrough is identified with “matrix mechanics,” sketched out in the summer of 1925 in a solitary stroke of genius by Werner Heisenberg, and then established on a solid foundation by the “triumvirate” of Heisenberg, Pascual Jordan (1902–1980), and Max Born. Early in 1926, the old quantum theory was independently revolutionized in an entirely different fashion by Erwin Schrödinger with “wave mechanics,” and shortly, the equivalence of matrix and wave mechanics was recognized. Since then, physicists have referred to the core of this new physics succinctly as “quantum mechanics.”

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Notes

  1. 1.

    Jammer, Development, 1966; Mehra/Rechenberg, Development, 1982; Darrigol, c-Numbers, 1992; Rechenberg, Werner Heisenberg, 2010; Meyenn, Entdeckung, 2011.

  2. 2.

    Sommerfeld, Ergänzungsband, 1929.

  3. 3.

    To Arthur March, 12. January 12, 1931. DMA, NL 89, 025. Also in ASWB II.

  4. 4.

    Kuhn, Structure, 1962. On the criticism of the concept of revolutionary crises, see Seth, Crisis, 2007.

  5. 5.

    Born/Heisenberg, Elektronenbahnen, 1923, p. 229.

  6. 6.

    From Born, January 5, 1923. DMA, HS 1977-28/A,34. Also in ASWB II.

  7. 7.

    From Heisenberg, January 15, 1923. DMA, HS 1977-28/A,136. Also in ASWB II.

  8. 8.

    From Pauli, June 6, 1923. Geneva, CERN-Archive. Also in ASWB II.

  9. 9.

    From Pauli, July 19, 1923. DMA, HS 1977-28/A,254.

  10. 10.

    To Else Rubinowicz, August 18, 1923.

  11. 11.

    Friedrich/Herschbach, Stern and Gerlach, 2005; Schmidt-Böcking/Reich, Otto Stern, 2011, Chap. VII

  12. 12.

    Sommerfeld, Magnetonenzahlen, 1923.

  13. 13.

    Sommerfeld, Theorie des Magnetons, 1923.

  14. 14.

    From Pauli, July 19, 1923. DMA, HS 1977-28/A,254.

  15. 15.

    From Heisenberg, December 8, 1923.DMA, NL 89, 009. Also in ASWB II.

  16. 16.

    To Landé, April 20, 1924. SBPK, Landé.

  17. 17.

    Forman, Doublet Riddle, 1968.

  18. 18.

    From Paschen, January 27, 1925. DMA, NL 89, 012.

  19. 19.

    To Millikan, February 9 1925. DMA, NL 89, 003. Also in ASWB II.

  20. 20.

    From Schrödinger, March 7, 1925. DMA, HS 1977-28/A,314. Also in ASWB II.

  21. 21.

    From Schrödinger, July 21, 1925. DMA, HS 1977-28/A,314. Also in ASWB II.

  22. 22.

    From Pauli, December 6, 1924. DMA, HS 1977-28/A,254. Also in ASWB II.

  23. 23.

    Meyenn, PaulisWeg I and II, 1980 and 1981; Massimi, Pauli’s Exclusion Principle, 2005.

  24. 24.

    Uhlenbeck/Goudsmit, Ersetzung, 1925.

  25. 25.

    Sommerfeld, Grundlagen, 1924, p. 1049.

  26. 26.

    An Bohr, 21. Januar 1923. Kopenhagen, NBA, Bohr. Also in ASWB II.

  27. 27.

    Sommerfeld, Atombau, 1924.

  28. 28.

    Hendry, Bohr-Kramers-Slater, 1981.

  29. 29.

    Heisenberg, Quantentheorie der Multiplettstruktur, 1925.

  30. 30.

    Heisenberg, Umdeutung, 1925.

  31. 31.

    Rechenberg, Werner Heisenberg, 2010, Chap. 5.

  32. 32.

    Quoted in Fölsing, Albert Einstein, 1993, p. 644.

  33. 33.

    Lecture delivered February 19, 1926. Wednesday Physics Colloquium. DMA, 1997-5115.

  34. 34.

    Rechenberg, Werner Heisenberg, 2010, p. 138.

  35. 35.

    From Heisenberg, November 18, 1924. DMA, HS 1977-28/A,136. Also in ASWB II.

  36. 36.

    Vote on the dissertation of Bechert to the Philosophical Faculty, 2. Section, May 18, 1925. Munich, UAM, OCI51p.

  37. 37.

    Vote on the dissertation of Ott to the Philosophical Faculty, 2. Section, July 12, 1924. Munich, UAM, OCI50p.

  38. 38.

    Vote on the dissertation of Hönl to the Philosophical Faculty, 2. Section, February 24, 1926. Munich, UAM, OCI 52p.

  39. 39.

    To Russell, July 3, 1925.Princeton, University Archive, C0045, box 63, folder 35.

  40. 40.

    Pauli, Wasserstoffspektrum, 1926.

  41. 41.

    To Wentzel, January 13, 1926. DMA, NL 89, 004.

  42. 42.

    To Edgar Meyer, 28. January 28, 1921. Zürich, University Archive, Papers of the Office of the Dean ALF. Also in ASWB II; Moore, Schrödinger, 1989, pp. 139ff.; Meyenn, Entdeckung, 2011, pp. 51ff.

  43. 43.

    From Schrödinger, January 29, 1926. DMA, NL 89, 013. Also in ASWB II; Meyenn, Entdeckung, 2011, pp. 170–172.

  44. 44.

    To Schrödinger, February 3, 1926. Carbon copy in DMA, NL 89, 004. Also in ASWB II; Meyenn, Entdeckung, 2011, pp. 173–175.

  45. 45.

    To Pauli, February 3, 1926. DMA, NL 89, 003. Also in ASWB II.

  46. 46.

    From Pauli, February 9, 1926. DMA, HS 1977-28/A,254. Also in ASWB II.

  47. 47.

    Meyenn, Entdeckung, 2011, pp. 176–208.

  48. 48.

    Schrödinger to W. Wien, February 22, 1926, quoted in Meyenn, Entdeckung, 2011, pp. 184–187.

  49. 49.

    Pauli to Jordan, April 12, 1926. quoted in WPWB I.

  50. 50.

    Sommerfeld, Lectures, 1926, p. 3. (“Schrödinger arrives at the same results as those obtained by the mechanics inaugurated by Heisenberg, but by a road that is presumably far simpler and more convenient […] his treatment is expressed in the language of the theory of vibrations.”)

  51. 51.

    To Johanna, March 11, 1926.

  52. 52.

    To Johanna, March 19, 1926.

  53. 53.

    To Johanna, March 23, 1926.

  54. 54.

    From Schrödinger, April 28, 1926. DMA, HS 1977-28/A,314. Also in ASWB II.

  55. 55.

    To Richardson, June 12, 1926. Austin, Ransom, Richardson.

  56. 56.

    To Schrödinger, July 10, 1926. DMA, NL 89, 025. On July 23, Schrödinger spoke, on “Foundations of Wave Mechanics” and the following day on “New Results in Wave Mechanics.” Physikalisches Mittwoch-Kolloquium. DMA, 1997-5115.

  57. 57.

    To Pauli, July 26, 1926. Geneva, CERN. Also in ASWB II.

  58. 58.

    From Einstein, August 21, 1926. DMA, HS 1977-28/A,78. Also in ASWB II.

  59. 59.

    Bethe in Eckert/Pricha/Schubert/Torkar, Geheimrat, 1984, p. 8.

  60. 60.

    Bethe, Sommerfeld’s Seminar, 2000.

  61. 61.

    Unsöld, personal communication, September 1, 1982.

  62. 62.

    Vote on the Dissertation of Unsöld to the Philosophical Faculty, 2nd section, December 11, 1926. Munich, UAM, OCI52p. Unsöld, Beiträge, 1927.

  63. 63.

    Eckert, Atommodelle, 2009.

  64. 64.

    From Schrödinger, April 28 and May 11, 1926. DMA, HS 1977-28/A,314. Also in ASWB II; from Ewald, July 15, 1926. DMA, NL 89, 007; to Ewald, July 20, 1926. DMA, NL 89, 001; from Heitler, August 29,1926. DMA, NL 89, 009.

  65. 65.

    Heitler, Interview by John L. Heilbron, March 18, 1963. AHQP. http://www.aip.org/history/ohilist/4662_1.html (31 January 2013). Heitler/London, Wechselwirkung, 1927.

  66. 66.

    Sopka, Quantum Physics, 1988; Assmus, Creation, 1993.

  67. 67.

    Victor Guillemin to KatherinSopka, 1972, quoted in Sopka, Quantum Physics, 1988, p. 2.41.

  68. 68.

    Pauling, Interview by John L. Heilbron, March 27, 1964. AHQP. http://www.aip.org/history/ohilist/3448.html (31 January 2013).

  69. 69.

    Pauli to Wentzel, December 5, 1926. In WPWB I.

  70. 70.

    Pauli, Gasentartung, 1927, p. 81.

  71. 71.

    Pauli to Rasetti, October, 1956. AHQP. (“[…] that one should make further application to other parts of metal theory like the Wiedemann–Franz law, thermoelectric effects, etc. As I was not eager to do that, he made then this further application himself.”).

  72. 72.

    Pauli toPeierls, July 3, 1931. Quoted in WPWB II.

  73. 73.

    Eckert, Elektronengas, 1989.

  74. 74.

    Lecture notes of Unsöld, now DMA.

  75. 75.

    To Paschen, July 25, 1927. DMA, NL 89, 003.

  76. 76.

    To Berliner, August 6, 1927. DMA, NL 89, 001. Sommerfeld, Elektronentheorie der Metalle, 1927.

  77. 77.

    Sommerfeld, Elektronentheorie der Metalle 1, 2, 1928.

  78. 78.

    To Millikan, November 28, 1927. DMA, NL 89, 025.

  79. 79.

    Houston, Interview by G. Phillips and W. J. King, March 3, 1964. AIP.

  80. 80.

    Houston, Leitfähigkeit, 1928.

  81. 81.

    Eckart, Elektronentheorie der Metalle, 1928.

  82. 82.

    To Millikan, March 26, 1928. DMA, NL 89, 025.

  83. 83.

    Eckert, Propaganda, 1987.

  84. 84.

    Hoddeson/Baym/Eckert, Development, 1987.

  85. 85.

    To Heisenberg, November 15, 1927. DMA, NL 89, 002.

  86. 86.

    Heisenberg to Pauli, August 1, 1929. In WPWB I.

  87. 87.

    From Heisenberg, February 6, 1929. DMA, HS 1977-28/A,136.

  88. 88.

    Planck to Lorentz, June 13, 1926. AHQP.

  89. 89.

    From Born, June 15, 1926. DMA, NL 89, 006. Also in ASWB II, S. 255.

  90. 90.

    Heilbron, Dilemmas, 1986, pp. 107–108.

  91. 91.

    Appointment Commission to the Philosophical Faculty of the Friedrich-Wilhelm-University, Berlin, June 18, 1926. UAB.

  92. 92.

    Minutes of the faculty meeting of November 18, 1926, and report of the Faculty to the Prussian Ministry of Culture of December 4, 1926. UAB.

  93. 93.

    From Nernst, March 19, 1927. DMA, NL 89, 019, folder 5,9.

  94. 94.

    From Windelband, March 24, 1927. DMA, NL 89, 019, folder 5,9. Also in ASWB II; to Johanna, March 30, 1927.

  95. 95.

    From Planck, April 7, 1927. DMA, NL 89, 019, folder 5,9. Also in ASWB II.

  96. 96.

    From Carathéodory, March 28, 1927. DMA, NL 89, 019, folder 5,9. Also in ASWB II.

  97. 97.

    From Gruber, March 28, 1927. DMA, NL 89, 019, folder 5,9.

  98. 98.

    From Vossler, March 30, 1927. DMA, NL 89, 019, folder 5,9. Also in ASWB I.

  99. 99.

    File notation, Prussian Ministry of Culture, April 29,1927. DMA, NL 89, 019. folder 5,9.

  100. 100.

    To the Dean, Philosophical Faculty, 2. Sektion, May 16. 1927. DMA, NL 89, 004. From the Bavarian Ministry of Culture, May 25, 1927 and June 20, 1927. DMA, NL 89, 019. folder 5,9.

  101. 101.

    To C. H. Becker, draft of an undated letter [between. May 31and June 11, 1927]. DMA, NL 89, 019. folder 5,9.

  102. 102.

    To the Prussian Ministry of Culture, June 11, 1927. DMA NL 89, 004. Also in ASWB II.

  103. 103.

    FromSchrödinger, July 14, 1927. DMA, NL 89, 019, folder 5,9.

  104. 104.

    Sommerfeld, Berlin, 1927.

  105. 105.

    From Goldenberger (Bavarian Minister of Culture), June 20, 1927. DMA, NL 89, 019, folder 5,9.

  106. 106.

    To Heisenberg, June 17, 1927. DMA, NL 89, 019, folder 5,9.

  107. 107.

    Völkischer Beobachter, July 8, 1927.

  108. 108.

    Vossische Zeitung, July 12, 1927.

  109. 109.

    Berliner Tageblatt, July 22, 1927.

  110. 110.

    Frankfurter Zeitung, July 21, 1927.

  111. 111.

    To Vossler, undated [ca. July, 1927].DMA, NL 89, 019, folder 5,9.

  112. 112.

    To Einstein, November 1, 1927. AEA, Einstein. Also in ASWB II.

  113. 113.

    Beller, Quantum Dialogue, 1999, pp. 39–49.

  114. 114.

    Mehra/Rechenberg, Development, 2000, Part 1, Chap. I.5; Janssen/Duncan, Transformations, 2009.

  115. 115.

    Rechenberg, Werner Heisenberg, 2010, Chap. 8.

  116. 116.

    To Franck, July 20, 1926. DMA, NL 89, 001. Also in ASWB II.

  117. 117.

    To Laue, July 22, 1926. DMA, NL 89, 002.

  118. 118.

    From Laue, July 27, 1926. DMA, NL 89, 010.

  119. 119.

    Sommerfeld, Elektronentheorie der Metalle und des Voltaeffektes, 1927.

  120. 120.

    Beller, Quantum Dialogue, 1999, Chap. 6. See also http://www.science20.com/don_howard/revisiting_einsteinbohr_dialogue (31 January 2013).

  121. 121.

    To Johanna, September 29, 1927.

  122. 122.

    To Levi-Cività, September 28, 1927. Rom, BANL, Levi-Cività.

  123. 123.

    To Johanna, October 1, 1927.

  124. 124.

    From Seeliger, November 20, 1927.D MA, NL 89, 013.

  125. 125.

    Grotrian, Darstellung, 1928, p. VII.

  126. 126.

    Sommerfeld, Ergänzungsband, 1929, Vorwort.

  127. 127.

    Vote on the Dissertation of Bethe to the Philosophical Faculty, 2. Section, July 24, 1928. UAM, OC Np1928. Sommerfeld, Ergänzungsband, 1929, pp. 241–250.

  128. 128.

    To Finlay Freundlich, January 14, 1927. DMA, NL 89, 001. Vote on the Dissertation of Unsöld to the Philosophical Faculty, 2. Sektion, December 11, 1926. UAM, OCI52p. Sommerfeld, Ergänzungsband, 1929, pp. 101–105.

  129. 129.

    Sommerfeld, Ergänzungsband, 1929, Foreword.

  130. 130.

    Zeitschrift für Elektrochemie und angewandte physikalische Chemie 34 (1928), pp. 425–426.

  131. 131.

    ToHund, February 29, 1928. DMA, NL 89, 002.

  132. 132.

    Sommerfeld, Bedeutung, 1928.

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Eckert, M. (2013). Wave Mechanics. In: Arnold Sommerfeld. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7461-6_9

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