1. Lande, “Das Versagen der Mechanik in der Quantentheorie,” Nwn, 11 (1923) 725-726; Lande, PZ, 24 (1923), 441-444; Born, Nwn, 11 (1923), 537-542Paschen, PZ, 24 (1923), 401-407.
2. Lande, PZ, 24 (1923), 441-444, on 441; and ZP, 19 (1923), 112-123 (rec. 16 Aug 23), on 123; Born, note 1, p. 542.
3. WH to Kurt Pflugel, 24 Nov [1923] (Pflugel Papers).
4. “Bekanntmachung uber das Diensteinkommen der Hochschulprofessoren,” Gesetz- und Verordnungsblatt fur den Freistaat Bayern, 1923, p. 313; “Gesetz ilber
die Festsetzung der Teuerungszuschlage der Staatsbeamten,” Gesetz- und V erordnungsblatt fur den Freistaat Bayern , 1923, 7.
5. “Teuerungszahlen der Gemeinden vom Juli 1923 bis Januar 1925,” Statistisches Jahrbuch fur das deutsche Reich, 44 (1924-1925), 261.
6. Hans Guradze and Karl Freudenberg, “Existenzminimum des geistigen Arbeiters im Marz-August 1923,” Jahrbiicher fur Nationalokonomie und Statistik, 121 (1923), 354-355.
7. “Teuerungszahlen,” note 5; “Lebensmittelpreise im Kleinhandel in einigen deutschen Stadten im Durchschnitt 1913/14 und vom Juli 1923 bis Januar 1925,” Statistisches Jahrbuch fur das deutsche Reich, 44 (1924-1925), 262.
8. W. Wien, “Ein Riickblick,” in Wien, Aus dem Leben und Wirken eines Physikers (Leipzig: Barth, 1930), pp. 1-50, on p. 47.
9. Born to Einstein, 7 Apr 1923 (EB, Briefw.).
10. Ibid.; “Personalakt Max Born” (UA Gottingen).
11. Brigitte Schroder-Gudehus, “The argument for the self-government and public support of science in Weimar Germany,” Minerva, 10 (1972), 537-570; Paul Forman, “The financial support and political alignment of physicists in Weimar Germany,” Minerva, 12 (1974), 39-66; and, for example, Friedrich Schmitt-Ott, “Die Kulturaufgaben und das Reich,” Internationale Monatsschrift fur Wissenschaft, Kunst und Technik, 11 (1919), 450-459; Georg Schreiber, Die Not der deutschen Wissenschaft und der geistigen Arbeiter (Leipzig: Quelle und Meyer, 1923).
12. This is argued in Forman, note 11.
13. Notgemeinschaft, Bericht I (1922), p. 38.
14. Ibid., pp. 38-39.
15. See Forman, note 11.
16. Records of Elektrophysikausschuss der Notgemeinschaft (BA Koblenz, R73), and Steffen Richter, Forschungsforderung in Deutschland 1920-1936. (Dusseldorf: VDI-Verlag, 1972).
17. WH to his parents, 20 Nov 1923. The stipend actually amounted to $12 per month, “Aufstellung. 27.10.23,” in records, note 16.
18. Ibid.; Richter, note 16; Born to Universitatskurator, 18 Jul 1925, in “Personalakt Dr. Heisenberg” (UA Gottingen, 4/Vc 317).
19. Ibid., and Courant to Universitatskurator, 30 Oct 1925 in Personalakt, note 18. On September 1, 1924, the Rentenmark was replaced by the Reichsmark, of equal value and same abbreviation. It lasted until 1948.
20. Notgemeinschaft, Bericht V (1926), p. 85. The statement was probably written by Planck.
21. WH to Kurt Pflugel, 21 Oct 1923 (Pflugel Papers). An overview of Bavarian political history during the Weimar era is given in Karl Schwend, Bayern zwischen Monarchie und Diktatur (Munich, 1954).
22. WH to Pflugel, 21 Oct 1923 (Pflugel Papers).
23. Pflugel to WH, 24 Oct [1923] (HP).
24. WH to Pflugel, 31 Oct 1923 (Pflugel Papers).
25. The dramatic effect was lost on the farmers near Gottingen, who astutely observed when it was all over: “Hei lebet noch!” (He’s still living!). WH to Pflugel,
24 Nov [1923] (Pflugel Papers).
26. Interview with Fr. Gottfried Simmerding, Munich, 17 Mar 1982. The story is unconfirmed.
27. Pflugel to WH, 12 Nov [1923] (HP). The influence of theology is evident in such statments.
28. WH to Pflugel, 24 Nov [1923] (Pfltigel Papers) and WH to his mother, 13 Nov [1923]. In the letter to Kurt, he also referred to Hitler’s “Operettennationalismus” (opera nationalism).
29. Wolfgang Riidel to WH, 22 Jan 1924 (HP).
30. WH to Pflugel, 24 Nov [1923]. Kurt responded by reiterating the decision of the Munich Pathfinders: “We had discussed this and found this position to be correct. ... In any case, neither words nor acts but work is now called for.” Pflugel to WH, 6 Dec 1923 (HP).
31. Much of the physics and the history of physics in this chapter is discussed by numerous authors from varying historical perspectives. This chapter relies primarily on the following works, to which the reader is referred for details: DC, “WH”; Serwer; MR 2, 106-124; Hendry, “BKS.”
32. A. Lande, ZP, 15 (1923), 189-205; E. Back, ZP, 15 (1923), 206-243. The formulas are equivalent to the modern formulas if one attributes the half-integral momentum to electron spin.
33. A. Sommerfeld, AP, 70 (1923), 32-62.
34. Thus, as before, the stationary-state energy of a Zeeman term is E = E 0 + gmj, where E 0 is the energy of a multiplet state corresponding to /, and
g = l +
/ 2 - 1/4 + R 2 — K 2 2 (J 2 ~ 1/4)
35. A. Lande, ZP, 11 (1922), 353-363, on 353-354.
36. Lande, note 32, p. 197.
37. Pauli to Lande, 26 Jul 1923.
38. WH to Pauli, 21 Leb [1923].
39. WH to Pauli, 26 Mar [1923],
40. There are 2 J + 1 m-values. If J increases by V 2 , the number of m-values increases by 1:2 (/ + V 2 ) + 1 = 2] + 2.
41. WH to Pauli, 26 Mar [1923].
42. Bohr to Lande, 3 Mar 1923 (AHQP 4, 1). A previously unpublished manuscript they produced is probably “Atomteoretiske Problemer” (1923, NBA) BCW 3 569-574.
43. Bohr, AP, 71 (1923), 228-288, rec. 15 Mar 1923 (BCW 4, 550-610).
44. In the doublet core model, the total angular momentum quantum number / of each state is / = k or k — 1. In Heisenberg’s core model, there are 2j* + 1 magnetic states, where j* = j - 1 / 2 ; thus 2(k - V 2 ) + 1 + 2(k - Vi ) + 1 = 2(2k - 1). In Lande’s vector model, there are 2 j magnetic states; thus 2k + 2(k — 1) = 2{k — 1).
45. Pauli to Bohr, 21 Leb 1924.
46. Pauli to Sommerfeld, 6 Jun 1923.
47. Pauli, ZP, 16 (1923), 155-164, rec. 26 Apr 23 (PCSP 2, 151-160).
48. Ibid., p. 164, and Pauli to Sommerfeld, 6 Jun 1923.
49. Ibid.; Pauli to Lande, 17 Aug [1923]; Pauli, note 47, p. 155. Pauli’s position is well summarized in Serwer.
50. Max Born and Friedrich Hund, Vorlesungen iiber Atommechanik, vol. 1 (Berlin: Sprmger-Verlag, 1925). The lectures were delivered during the 1923-1924 school year.
51. WH to Pauli, 9 Oct 1923.
52. Ibid., and WH to Bohr, 22 Dec [1923] (BSC 11, 2).
53. = F(J), where the integral is taken from /' =] — 1/2 to /' = / + V 2
so H cl (]) = dF(J)/dJ. Heisenberg then replaced F(J) with H qu and the differential with a difference.
54. This discussion derives from the letters in notes 51 and 52 and from Heisenberg’s paper, “Uber eine Abanderung der formalen Regeln der Quantentheorie beim Problem der anomalen Zeemaneffekte” (rec. 13 Jun 24), HCW Al, 289-305.
55. WH, note 51.
56. Lande, note 32, p. 200; also Pauli to Lande, 23 Sep 1923.
57. Hund, “Mathematisches Tagebuch,” entry for 16 Apr 1923 (Hund papers, Gottingen).
58. Ibid., entry for 9 Oct 1923; and WH, “Uber ein neues Quantenprinzip und dessen Anwendung auf die Theorie des anomalen Zeemaneffektes,” draft manuscript (1923), HA and AHQP 45, 8.
59. WH to his mother, 7 Nov 1923; WH to his father, 29 Nov [1923]. Runge even lectured on Heisenberg’s theory before Gottingen’s Mathematische Gesellschaft.
60. WH to his father, 29 Nov [1923],
61. WH to Pauli, 7 Dec 1923; the manuscript was that in note 58. WH to Lande,
7 and 13 Dec 1923 (AHQP 6, 2). Heisenberg also wrote Sommerfeld of his new theory, 12 Dec 1923 (SN).
62. Indicated in WH to Bohr, 22 Dec [1923] (BSC 11, 2). Heisenberg’s earlier letters to Bohr were all in Fraktur (Gothic) manuscript.
63. WH to Bohr, 22 Dec [1923] (BSC 11, 2). Heisenberg soon expressed the hope that even half integers would find a basis in the new principle. WH to Bohr, 3 Feb [1924] (BSC 11, 2).
64. Bohr to WH, 31 Jan 1924 (BSC 11, 2).
65. Pauli to Lande, 14 Dec [1923], to Bohr, 21 Feb 1924, and to Kramers, 19 Dec 1923.
66. A report of the meeting is given in “Gemeinschaftliche Tagung des Gauvereins Niedersachsen der Deutschen Physikalischen Gesellschaft in Braunschweig am 9. und 10. Februar 1924,” Deutsche Physikalische Gesellschaft, Verb., 5 (1924), 7-11. The three lectures were by Hund (“Rydbergkorrektion und Grosse des Atomrumpfes”), WH (“Quantitatives uber die Deformierbarkeit edelgasahnlicher Ionen”), and Born (“Der Einfluss der Ionendeformation auf physikalische und chemische Konstanten”).
67. Pauli to Bohr, 11 Feb 1924.
68. An entry in Hund’s diary at that time may be an example of this kind of reasoning: “The quantum effects are better understood with half-integral K than with whole integrals.” Hund, note 57, entry for 17 Jan 1924.
69. Pauli, note 65.
70. WH to his parents, 15 Mar [1924]. He arrived that day.
71. Ibid., and Bohr to Wickliffe Rose, carbon copy, 16 Apr 1924 (BGC).
72. WH to his parents, 20 and 27 Mar [1924]. Bohr did not apply to Rose for Werner’s funding until 16 Apr 1924 (BGC) and 15 May 1924 (RAC, IEB series 1, Box 50, W. Heisenberg file, 1924-1929).
73. WH to his parents, 23 Mar [1924],
74. Ibid.
75. WH to his parents, 27 Mar [1924],
76. Post-doctoral physicist Slater was on a Sheldon Traveling Fellowship. He stayed in Copenhagen until April 1924, according to data in Robertson, pp. 156-159; the other two Americans were probably F. C. Hoyt and H. C. Urey.
77. Bohr, Kramers, and Slater, Phil. Mag., 47 (1924), 785-802 dated January 1924 (BCW 5, 101-118; English version in Waerden, pp. 159-176); Kramers, Nature, 133
(1924), 673-676, dated 25 March 1924. Heisenberg reported (note 70) that on his arrival Bohr handed him two papers to read; they were most probably these.
78. WH, “Die Entwicklung der Quantentheorie 1918-1928” (1929), HCW B, 109-115.
79. This distinction and the BKS theory are described more fully in Hendry,
“BKS,” and in Dresden, pp. 159-215.
80. Ladenburg, ZP, 4 (1921), 451-468.
81. Pauli to Eddington, 20 Sep 1923.
82. Slater to Kramers, 8 Dec 1923 (AHQP 8, 10); Slater, Nature, 113 (1924), 307-308.
83. BKS, note 77 in Waerden, p. 165. Slater did not concur with the full theory. Slater, Nature, 116 (1925), 278; Slater, Phys. Rev., 25 (1925), 395-428.
84. The contrast is indicated in WH to Pauli, 4 Mar [1924], and WH to Bohr, Munich, 16 Apr [1924] (BSC 11, 2).
85. WH to Pauli, 26 Mar 1924.
86. WH to Bohr, 15 May 1924 (BSC 11, 2).
87. WH, to his mother, 31 May [1924], There is a play on words here. The usual notice reads “Hund entlaufen,” Hund (dog) being Born’s other assistant.
88. Born and WH, ZP, 23 (1924), 388-410 rec. 22 Mar 24, (HCW Al, 247-269); WH, ZP, 26 (1924), 196-204, rec. 4 Jun 24, (HCW Al, 280-288); Born and Hund, Vorlesungen, note 50, in which Born thanked Dr. Heisenberg for advice and calculations; and Born, “Uber Quantenmechanik,” ZP, 26 (1924), 379-395 (English translation in Waerden, pp. 181-198). Born again thanked Heisenberg for “much advice and help with the calculations” (Waerden, p. 182).
89. WH to Lande, 22 Dec 1923 (AHQP 6, 2).
90. The rule is described in more detail in DC, “WH,” 296-302; and MR 2,117-120.
91. WH to Lande, 6 May 1924 (AHQP 6, 2); Lande and WH, ZP, 25 (1924), 279-286, on 286, rec. 18 May 24 (HCW Al, 270-277); and WH, note 54, p. 301.
92. WH to Bohr, 15 May 1924 (BSC 11, 2).
93. Heisenberg wrote Lande of a difficulty for the new scheme posed by Lande’s “absolute value rules.” Bohr, Heisenberg claimed, “came here because of this matter.” WH to Lande, 15 Jun [1924] (AHQP 6, 2).
94. Rose to Bohr, 2 Jun and 10 Jun 1924 (RAC, IEB series 1, Box 50,
W. Heisenberg file); Bohr to Rose, 5 Jul 1924 (RAC, IEB Denmark, Box 2146,
Bolder 403).
95. Born to Bohr, 16 Apr 1924 (BCW 5, 299).
96. Kramers, note 77.
97. Born, note 88 (Waerden, p. 190).
98. Ibid., p. 191.
99. WH to Lande, 15 Jun [1924] (AHQP 6, 2).
100. Born, note 88 (Waerden, p. 198).
101. WH to his mother, 5 Jun 1924.
102. WH to his parents, 8 Jun [1924].
103. WH to Pauli, 8 Jun [1924]; WH to his parents, 8 Jun [1924],
104. Einstein to Born, 29 Apr 1924 (EB, Briefw.).
105. Born, note 88 (Waerden, p. 189).
106. WH to Lande, 6 Jul [1924] (AHQP 6, 2).
107. Bohr to WH, 5 Jul 1924 (BSC 11, 2).
108. Personalakt Dr. Heisenberg (UA Gottingen, 4/Vc 317). Heisenberg’s venia legendi for the field of theoretical physics was not officially conferred until 10 Oct 1924 (Certificate in HA).
109. WH to Bohr, 5 Jul and 25 Aug [1924] (BSC 11, 2).