From the 1926 Wave Mechanics to a Second-Quantisation Theory: Schrödinger’s New Interpretation of Wave Mechanics and Microphysics in the 1950’s

  • Salvo D’Agostino
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 213)


Erwin Schrödinger (1887–1961) based his initial scientific program on a matter-waves interpretation of the psi-waves of his 1926 wave mechanics.1 In March 1926 he proposed the so-called electrodynam-ic interpretation2 (psi-square taken as proportional to charge density) and shortly afterwards, the beat-interpretation of atomic radiation emission3 (atomic radiation as a beat phenomenon between stationary psi-waves, the emission-frequency equal to the beat frequency).


Quantum Mechanic Classical Physic Wave Mechanics Clear Model Beat Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schrödinger, “Quantisierung als Eigenwertproblem”, Annalen der Physik, 79; Schrödinger[1926]a.Google Scholar
  2. 2.
    Schrödinger [1926] a; Vierte mitteilung. Google Scholar
  3. 3.
    Schrödinger [1926] a, Erste Mitteilung, Sect 3.Google Scholar
  4. 4.
    Born [1926].Google Scholar
  5. 5.
    Schrödinger [1926] b.Google Scholar
  6. 6.
    Schrödinger [1929] 15–16.Google Scholar
  7. 7.
    Schrödinger [1929] 15.Google Scholar
  8. 8.
    Schrödinger [1932]; Schrödinger [1987] 20–36.Google Scholar
  9. 9.
    Schrödinger [1935].Google Scholar
  10. 10.
    Fine [1986] 64–85.Google Scholar
  11. 11.
    According to Ruger: “Affine theory in the Forties and QM in the Thirties and Forties formed a complex of problems out of which grew, in the 1940’s, Schrödinger’s affine field theory and his ‘late’ interpretation of QM” (Rüger [1988] 378).Google Scholar
  12. 12.
    The method of second-quantisation was developped in 1927 by RA.M. Dirac for particles obeying Bose statistics, and later in 1928 extended to Fermi particles by E.Wigner and R Jordan.Google Scholar
  13. 13.
    Schrödinger [1928]; Schrödinger [1984], Vol. 3, 185–206, 185.Google Scholar
  14. 14.
    Schrödinger [1984], Vol. 3, 205.Google Scholar
  15. 15.
    C.N.Yang emphasises Schrödinger’s reluctance at that time to use complex numbers in the role of physical quantities: Yang, “Square roots of Minus One, Complex Phases and E.Schrödinger” in: Kilmister [1987] 53–64, 54.Google Scholar
  16. 16.
    Schrödinger, “What is an elementary particle” in Schrödinger [1984] 456–463, 459.Google Scholar
  17. 17.
    Schrödinger [1984] 459.Google Scholar
  18. 18.
    Schrödinger [1984] 459.Google Scholar
  19. 19.
    Schrödinger[1953] 16.Google Scholar
  20. 20.
    Schrödinger [1953] 24.Google Scholar
  21. 21.
    Schrödinger [1953] 24. Schrödinger quotes his 1950 paper in Endeavour and his 1951 paper in the Austrian Journal Die Pyramide. Google Scholar
  22. 22.
    Schrödinger[1953]24.Google Scholar
  23. 23.
    Schrödinger [1953] 28.Google Scholar
  24. 24.
    Appendix 1 in this section.Google Scholar
  25. 25.
    Appendix 2, in this section.Google Scholar
  26. 26.
    Schrödinger [1984] 295–297, 296.Google Scholar
  27. 27.
    Fine mantains (Fine [1986]) that Schrödinger addressed the same critique to Einstein’s statistical interpretation of QM.Google Scholar
  28. 28.
    Schrödinger [1932] 8; Schrödinger [1987] 31.Google Scholar
  29. 29.
    Fine [1986] 81–85.Google Scholar
  30. 30.
    Schrödinger [1951].Google Scholar
  31. 31.
    Schrödinger [1951] 54.Google Scholar
  32. 32.
    Schrödinger [1951] 55.Google Scholar
  33. 33.
    Schrödinger [1951] 55.Google Scholar
  34. 34.
    Schrödinger [1951] 56.Google Scholar
  35. 35.
    Schrödinger [195] 54.Google Scholar
  36. 36.
    Schrödinger [1951] 19.Google Scholar
  37. 37.
    Schrödinger [1951] 57.Google Scholar
  38. 38.
    Schrödinger [1951] 17, 18.Google Scholar
  39. 39.
    On many occasions in his writings, Schrödinger refers to his teacher Franz Exner as the first to advance doubts on energy conservation at the atomic scale and, more generally, proposed a non-deterministic view of the microworld, and a rejection of statistics in the classical sense. An early referenceto Exner is in: Schrödinger [1984] Vol. 4, 295–297, 296–297.Google Scholar
  40. 40.
    Schrödinger [1951] 21.Google Scholar
  41. 41.
    Schrödinger [1951] 47, 48.Google Scholar
  42. 42.
    Schrödinger [1951] 48.Google Scholar
  43. 43.
    “I will not say that Kant’s idea [transcendentalism of space and time as forms of “mental intuition” (Anshauung)]was completely wrong, but it was certainly too rigid and needed modification when new possibility came to light.This new possibility is offered by Einstein’s restricted theory of relativity”; in: Schrödinger [1951] 48.Google Scholar
  44. 44.
    Schrödinger [1951] 65.Google Scholar
  45. 45.
    Schrödinger [1951] 53.Google Scholar
  46. 46.
    Schrödinger [1951] 63.Google Scholar
  47. 47.
    Schrödinger [1951] 1–2.Google Scholar
  48. 48.
    Schrödinger, “The meaning of the Wave Mechanics” in: Einstein, De Broglie et al.[1953] 16.Google Scholar
  49. 49.
    Schrödinger [1951] 28.Google Scholar
  50. 50.
    Schrödinger [1951] 28–29.Google Scholar
  51. 51.
    Schrödinger [1951] 29.Google Scholar
  52. 52.
    Schrödinger [1951] 40.Google Scholar
  53. 53.
    Schrödinger [1951] 32–33.Google Scholar
  54. 54.
    Schrödinger [1951] 40.Google Scholar
  55. 55.
    Schrödinger [1951] 41.Google Scholar
  56. 56.
    Schrödinger [1951] 29.Google Scholar
  57. 57.
    Schrödinger [1951] 40. In “Are there Quantum Jumps ?”, Schrödinger criticised Bohr’s theory on the point that, in this theory, atomic radiative transitions occur instantaneously.Google Scholar
  58. 57a.
    Schrödinger “Are there Quantum Jumps?” in: Schrödinger [1984] 478–502, 483.Google Scholar
  59. 58.
    Schrödinger [1951] 39.Google Scholar
  60. 59.
    One could here refer to one of Heisenberg’s numerous statements against Schrödinger’s positions; e.g., on the electron transition between two stationary levels in an atom: “Schrödinger therefore rightly emphasises that… such processes can be conceived of as being more continuous then in the usual picture, but such an interpretation cannot remove the element of discontinuity that is found everywhere in atomic physics: any scintillation screen or Geiger counter demonstrates this element at once. In the usual interpretation of quantum mechanics is contained the transition from the possible to the actual. Schrödinger himself makes no counterproposal as to how he intends to introduce this element of discontinuity, everywhere observable, in a different manner from the usual interpretation” (Heisenberg [1958] 84). Evidently, Heisenberg did not agreewith Schrödinger’s proposal of two levels of languags, and with his idea that an element of discontinuity is acceptable at the observational level.Google Scholar
  61. 60.
    Schrödinger [1951] 41. The highly generalised type of field equations are the wave functionals resulting from second quantisation.Google Scholar
  62. 61.
    Schrödinger [1951] 19.Google Scholar
  63. 62.
    Schrödinger [1958] 169.Google Scholar
  64. 63.
    Schrödinger [1958] 169.Google Scholar
  65. 65.
    Schrödinger [1951] 40.Google Scholar
  66. 66.
    Schrödinger [1951] 26. The passage is quoted with the author’s comment in: Arendt [1958].Google Scholar
  67. 66a.
    Arendt [1988] 213. In Arendt’s view: “the new universe of science presented by Schrödinger is not only practically inaccessible but unthinkable as well”. As we have seen, Schrödinger in effect distinguishes between the capacity of thinking a perfect model from the conviction that the model represent the true universe of science. A perfect model is thinkable, while the latter is not only unthinkable but even beyond such ideas as Kant’s Noumenon. For Schrödinger, the metaphorical example of a winged lion symbolises a partially thinkable objec.Google Scholar
  68. 67.
    Schrödinger [1951] 25.Google Scholar
  69. 68.
    Schrödinger might refer to the following passage in Boltzmann’s “On the significance of theories: ”I am of the opinion that the task of theory consists in constructing a picture of the external world that exists purely internally and must be our guiding star in all thought and experiment; that is in completing, as it were, the thinking process and carrying out globally what on a small scale occurs within us whenever we form an idea” (Boltzmann [1974] 33).Google Scholar
  70. 69.
    Schrödinger [1951] 25.Google Scholar
  71. 70.
    On such matters, Schrödinger preferred the positivist’s fidelity to phenomena, ignoring the quest for knowledge which is not attainable in principle: “I fully agree [with the positivist] that the uncertainty relation has nothing to do with incomplete knowledge. It does reduce the amount of information attainable about a particle as compared with views held previously. The conclusion is that these views were wrong and that we must give them up”; (Schrödinger [1950] 456).Google Scholar
  72. 71.
    For an interesting thesis on Hertz’s Bild, see: Chevalley [1991] 549 ff.Google Scholar
  73. 72.
    Hertz: “Die Bilder von welche wir reden, sind unsere Vorstellungen von den Dingen; sie haben mit den Dingen die eine wesentlich Übereinstimmung, welche in der Erfüllung der genanten Forderung liegt, aber es ist für ihren Zweck nicht nötig, daß sie irgend eine weitere Übereinstimmung mit den dingen haben” (Hertz[1895], Einleitung, 1–2). Let us compare this passage with Schrödinger’s statement in 1928: “Tch glaube dazu kann man doch einige erkenntnistheoretische Trostworte sagen. Wir dürfen nicht vergessen, daß die Bilder und Modelle schließlich doch keinen anderen Zweck haben, als alle prinzipiell möglichen Beobachtungen an ihnen aufzuhangen”(Schrödinger [1984] 294).Google Scholar
  74. 73.
    Schrödinger [1951] 24.Google Scholar
  75. 74.
    Schrödinger [1958].Google Scholar
  76. 75.
    Schrödinger [1927].Google Scholar
  77. 76.
    I am grateful to Helge Kragg for this objection.Google Scholar
  78. 77.
    Some of these themes, not all of them in line with his predominant interest of the moment, Schrödinger just touched on and left unexplored. One example is offered by a letter from F. London to Schrödinger, quoted by C. N.Yang in his “Square root of -1, Complex Phases and Schrödinger”; in: Kilmister [1987] 53–63, 62.Google Scholar
  79. 78.
    Schrödinger [1953] 28.Google Scholar
  80. 79.
    J. Dorling inclines to consider the physicists’ dismissal of Schrödinger’s views as “largely a sociological accident”; in: Dorling [1987] 39.Google Scholar
  81. 80.
    See among others, the papers by J. Dorling, J. S. Bell and C. N. Jungin; in: Kilmister [1987]. See also: A.O. Barut, Ann. der Physik, (Schrödinger issue [1987]) and Foundation of Physics, (Schrödinger issue [1987]).Google Scholar
  82. 81.
    Schrödinger [1984] 461.Google Scholar
  83. 82.
    Schrödinger [1935] 65.Google Scholar
  84. 83.
    Landau & Lifshitz [1958] 221.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Salvo D’Agostino
    • 1
  1. 1.Università “La Sapienza”RomaItaly

Personalised recommendations