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Pauli’s Electron in Ehrenfest and Bohm Theories, a Comparative Study
Version 1
: Received: 21 December 2022 / Approved: 12 January 2023 / Online: 12 January 2023 (07:01:35 CET)
A peer-reviewed article of this Preprint also exists.
Yahalom, A. Pauli’s Electron in Ehrenfest and Bohm Theories, a Comparative Study. Entropy 2023, 25, 190. Yahalom, A. Pauli’s Electron in Ehrenfest and Bohm Theories, a Comparative Study. Entropy 2023, 25, 190.
Abstract
Electrons moving at slow speeds much lower that the speed of light are described by a wave function which is a solution of Pauli’s equation. This is a low velocity limit of the relativistic Dirac equation. Here we compare two approaches, one which is the more conservative Copenhagen’s interpretation denying a trajectory of the electron but allowing a trajectory to the electron expectation value through Ehrenfest theorem. The said expectation value is of course calculated using a solution of Pauli’s equation. A less orthodox approach is championed by Bohm, and attributes a velocity field to the electron also derived from the Pauli wave function. It is thus interesting to compare the trajectory followed by the electron according to Bohm and its expectation value according to Ehrenfest. Both similarities and differences will be considered.
Keywords
Spin; Quantum Mechanics; Ehrenfest Theorem
Subject
Physical Sciences, Quantum Science and Technology
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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