Time-dependent conserved operators for Schrödinger equation withconstant electromagnetic field and quantization of resistance

• Jorge A. Lizarraga ^[1]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 72, Nº. 2, 2026
• Idioma: inglés
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• Resumen

  • Two systems are studied: the first one involves a charged particle under the influence of a constant electric field, and the second one involvesa charged particle under the influence of a constant electromagnetic field. For both systems, it is possible to find time-dependent conservedoperators that can be used to derive time-dependent solutions to the complete Schr ̈odinger equation. These conserved operators are employedto define the symmetries of the system. An argument of invariance of the wave function under the action of a unitary operator leads to thequantization of resistance and resistivity, in integer multiples of the von Klitzing’s constant, for the first and second case respectively.