Time Evolution of Energy States

Richard Oldani

doi:10.20944/preprints202305.0952.v6

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preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202305.0952.v6

Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed

Time Evolution of Energy States

Richard Oldani

Version 1 : Received: 12 May 2023 / Approved: 12 May 2023 / Online: 12 May 2023 (13:38:11 CEST)
Version 2 : Received: 23 June 2023 / Approved: 30 June 2023 / Online: 3 July 2023 (13:36:33 CEST)
Version 3 : Received: 27 October 2023 / Approved: 27 October 2023 / Online: 30 October 2023 (12:19:56 CET)
Version 4 : Received: 21 November 2023 / Approved: 22 November 2023 / Online: 23 November 2023 (16:36:39 CET)
Version 5 : Received: 11 December 2023 / Approved: 12 December 2023 / Online: 13 December 2023 (06:11:17 CET)
Version 6 : Received: 29 December 2023 / Approved: 29 December 2023 / Online: 29 December 2023 (10:37:10 CET)
Version 7 : Received: 2 April 2024 / Approved: 3 April 2024 / Online: 5 April 2024 (03:54:56 CEST)

How to cite: Oldani, R. Time Evolution of Energy States. Preprints 2023, 2023050952. https://doi.org/10.20944/preprints202305.0952.v6 Oldani, R. Time Evolution of Energy States. Preprints 2023, 2023050952. https://doi.org/10.20944/preprints202305.0952.v6

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MDPI and ACS Style

Oldani, R. Time Evolution of Energy States. Preprints 2023, 2023050952. https://doi.org/10.20944/preprints202305.0952.v6

APA Style

Oldani, R. (2023). Time Evolution of Energy States. Preprints. https://doi.org/10.20944/preprints202305.0952.v6

Chicago/Turabian Style

Oldani, R. 2023 "Time Evolution of Energy States" Preprints. https://doi.org/10.20944/preprints202305.0952.v6

Abstract

In order to describe the time evolution of energy states we choose to abandon the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a more fundamental, relativistically correct Lagrangian method based on theories originally proposed by Dirac and Einstein. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, the function of the simplest quantum mechanical system an electron cyclotron, atomic clocks, matrix mechanics, chaos theory, and evolutionary biology.

Keywords

non-relativistic quantum mechanics; relativistic quantum mechanics; Hamilton’s principle; energy; symmetry

Subject

Physical Sciences, Theoretical Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 29 December 2023
Commenter: Richard Oldani
Commenter's Conflict of Interests: Author

Comment: Equations 1) and 2) have been corrected.

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