The Development of Elementary Quantum Theory by Herbert Capellmann

Author:Herbert Capellmann
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(6.10)

But this equation cannot serve as a proper wave equation, since it contains the energy explicitly, restricting the possible solutions to harmonic behavior. The “wave equation” is equivalent to the time independent eigenvalue equation.

Of particular interest is Schrödinger’s first reference to the quantum theory of Born , Heisenberg , and Jordan and the description of Schrödinger’s attitude towards the new mode of thought it contains. Schrödinger criticizes the elimination of continuity in space and time; he argues that - from the philosophical point of view - this constitutes total capitulation, which he refuses:“We are not really able to change the modes of thought and if we cannot understand within these modes of thought, then we cannot understand at all.” (“Denn wir können die Denkformen nicht wirklich ändern und was wir innerhalb derselben nicht verstehen können, das können wir überhaupt nicht verstehen.”) A discussion contrasting the attitudes of Einstein , Bohr , Born, and Schrödinger will be given in a later chapter.

Schrödinger’s third publication of the series (Ann. Phys. 79, 734–756 1926, rec. 18 March 1926) contains the explicit connection to matrix mechanics and the transition from the commutation relation to the continuous “r representation” and . But Schrödinger discards a full equivalence of the two approaches, insisting on the physical significance of wave functions , which he sees as the essential element; wave mechanics should be understood as an extension and part of classical field theories. Concerning matrix mechanics Schrödinger reaffirms his disagreement about physical content and mathematical formulation; he states that he felt deterred, if not to say repelled, by the apparently “very difficult methods of transcendental algebra and the lack of illustrative clarity”(“ich fühlte mich durch die mir sehr schwierig scheinenden Methoden der transzendenten Algebra und durch den Mangel an Anschaulichkeit abgeschreckt, um nicht zu sagen abgestossen”).

Schrödinger’s forth publication of the series (Ann. Phys. 79, 734–756 1926, rec. 10 May 1926) contains the wave mechanical version of time independent perturbation theory (equivalent to matrix mechanical perturbation theory of “BHJ”) and its application to the Stark effect of the Balmer series, reproducing the results Pauli had obtained in his matrix solution of the hydrogen problem.

In his 5’th publication of the series (Ann. Phys. 81, 109–139, 1926; rec. 21 June 1926) Schrödinger recognizes that the time dependent “wave equation” of the second publication cannot be used as general wave equation, since energy E is contained explicitly.

Schrödinger makes several further guesses at wave equations, which originate from the application of the operator to the eigenvalue equation for a second time, leading to an equation containing forth order derivatives with respect to position. Again simple harmonic behavior with frequency is provisionally assumed (equivalent to: ) leading to

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