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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)

Abstract

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).

Keywords

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.

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Notes

  1. 1.
    Schrödinger, “Quantisierung als Eigenwertproblem”, Annalen der Physik, 79; Schrödinger[1926]a.Google Scholar
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    Schrödinger [1926] a; Vierte mitteilung. Google Scholar
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    Schrödinger [1926] a, Erste Mitteilung, Sect 3.Google Scholar
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    Schrödinger [1926] b.Google Scholar
  6. 6.
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  8. 8.
    Schrödinger [1932]; Schrödinger [1987] 20–36.Google Scholar
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    Schrödinger [1935].Google Scholar
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  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
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    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
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    “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
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    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
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    Schrödinger “Are there Quantum Jumps?” in: Schrödinger [1984] 478–502, 483.Google Scholar
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  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
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    Schrödinger [1951] 41. The highly generalised type of field equations are the wave functionals resulting from second quantisation.Google Scholar
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    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
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  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
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    Schrödinger [1951] 25.Google Scholar
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    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
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    For an interesting thesis on Hertz’s Bild, see: Chevalley [1991] 549 ff.Google Scholar
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    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
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    Schrödinger [1951] 24.Google Scholar
  75. 74.
    Schrödinger [1958].Google Scholar
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    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

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