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Quantum Potential in time-dependent supersymmetric quantum mechanics

Strange, Paul (2021) Quantum Potential in time-dependent supersymmetric quantum mechanics. Physical Review A: Atomic, Molecular and Optical Physics, 104 (06). Article Number 062213. ISSN 1050-2947. E-ISSN 2469-9926. (doi:10.1103/PhysRevA.104.062213) (KAR id:92439)

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Abstract

If a wave function is written in polar form it becomes possible to write the Schrödinger equation of nonrelativistic quantum mechanics in a form analogous to the classical Hamilton-Jacobi equation with an extra term known as the quantum potential. Time-dependent supersymmetry is a procedure for finding new solutions of the Schrödinger equation if one solution is known. In this paper a time-dependent supersymmetry transformation is applied to a wave function in this polar form and it is shown that the classical potential plus the quantum potential is a conserved quantity under this transformation under certain circumstances. This leads to a modification of our view of the role of the quantum potential and also to a deeper appreciation of the function of a supersymmetry transformation.

Item Type: Article
DOI/Identification number: 10.1103/PhysRevA.104.062213
Uncontrolled keywords: Physics of Quantum Materials
Subjects: Q Science
Q Science > QC Physics > QC174.12 Quantum theory
Divisions: Divisions > Division of Natural Sciences > Physics and Astronomy
Depositing User: Paul Strange
Date Deposited: 24 Dec 2021 10:46 UTC
Last Modified: 04 Jan 2022 14:19 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/92439 (The current URI for this page, for reference purposes)
Strange, Paul: https://orcid.org/0000-0001-5818-8032
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