Schrödinger’s field equation

The intrinsic and dynamic kinetic energies and the potential energies of electron states in the hydrogen atom were determined using the operator formalism in Schrödinger’s nonrelativistic equation. Intrinsic energies were determined using the momentum operator, while for ℓ ≠ 0, the additional dynamic energies of the spinning fields were determined using the angular momentum operator. All 10 states up to the principal quantum number n = 3 and all 4 m states of n = 7, l = 3 were analyzed. The two forms of kinetic energy can only be explained with an electron field representation. All total kinetic and potential energies conformed with the well-known 1/n2 rule. Angular momentum analysis of the 2P1/2 state provided a field spinning rate; in addition, the dynamic kinetic energy of the spinning field determined by both operator analysis and explicit calculation based on the spinning rate gave the same energy results.

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Publication Details

Journal
AIP Advances
Published
2025-02-01
DOI
https://doi.org/10.1063/5.0244520
Primary Topic
Cold Atom Physics and Bose-Einstein Condensates
Type
article
Field-Weighted Citation Impact
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article

Schrödinger’s field equation

J. A. Mroczkowski
AIP Advances
Cold Atom Physics and Bose-Einstein Condensates
article

Schrödinger’s field equation

J. A. Mroczkowski
article en

Abstract

The intrinsic and dynamic kinetic energies and the potential energies of electron states in the hydrogen atom were determined using the operator formalism in Schrödinger’s nonrelativistic equation. Intrinsic energies were determined using the momentum operator, while for ℓ ≠ 0, the additional dynamic energies of the spinning fields were determined using the angular momentum operator. All 10 states up to the principal quantum number n = 3 and all 4 m states of n = 7, l = 3 were analyzed. The two forms of kinetic energy can only be explained with an electron field representation. All total kinetic and potential energies conformed with the well-known 1/n2 rule. Angular momentum analysis of the 2P1/2 state provided a field spinning rate; in addition, the dynamic kinetic energy of the spinning field determined by both operator analysis and explicit calculation based on the spinning rate gave the same energy results.

AIP AdvancesVol. 15(2)
Bedford Research Foundation (US), Université Bourgogne Franche-Comté (FR)
Openalex Percentile: Top 97%
Cold Atom Physics and Bose-Einstein Condensates
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