Nonlinear Pauli equation

Sergey A. Rashkovskiy; Sergey A. Rashkovskiy

doi:10.3934/cam.2024005

Communications in Analysis and Mechanics

2024, Volume 16, Issue 1: 94-120. doi: 10.3934/cam.2024005

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Research article

Nonlinear Pauli equation

Sergey A. Rashkovskiy ^,

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Vernadskogo Ave., 101/1, Moscow, 119526, Russia

Received: 15 June 2023 Revised: 15 January 2024 Accepted: 16 January 2024 Published: 18 January 2024
81Sxx, 81P10, 81Q80

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an EW in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an EW is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.
- classical field theory,
- unified Maxwell-Pauli theory,
- non-linear Pauli equation,
- non-linear Schrödinger equation,
- spin behavior in a magnetic field
Citation: Sergey A. Rashkovskiy. Nonlinear Pauli equation[J]. Communications in Analysis and Mechanics, 2024, 16(1): 94-120. doi: 10.3934/cam.2024005

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Abstract

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an EW in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an EW is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

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