Time-dependent conserved operators for non-relativistic Schrödinger equation with electromagnetic field and quantization of resistance

• URL: http://arxiv.org/abs/2404.05115v1
• Date: Mon, 8 Apr 2024 00:28:57 GMT
• Title: Time-dependent conserved operators for non-relativistic Schrödinger equation with electromagnetic field and quantization of resistance
• Authors: Jorge A. Lizarraga,
• Abstract summary: Two systems are studied: the first one involves a charged particle under the influence of a constant electric field, and the second one involves a charged particle under the influence of a constant electromagnetic field. For both systems, it is possible to find time-dependent conserved operators that can be used to derive time-dependent solutions to the complete Schr"odinger equation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Two systems are studied: the first one involves a charged particle under the influence of a constant electric field, and the second one involves a charged particle under the influence of a constant electromagnetic field. For both systems, it is possible to find time-dependent conserved operators that can be used to derive time-dependent solutions to the complete Schr\"odinger equation. These conserved operators are employed to define the symmetries of the system. An argument of invariance of the wave function under the action of a unitary operator leads to the quantization of resistance and resistivity, in integer multiples of the von Klitzing's constant, for the first and second cases respectively.

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