Canonical equivalence of a particle in a magnetic field to a simple oscillator

2023/04/01 by Henryk Gzyl, Gzyl, Henryk
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2304.00401

openalex publication_date 2023/04/01 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28

Abstract

It is proved that a classical (respec. quantum) system consisting of a particle in a constant magnetic field is canonically (respec. unitarily) equivalent to a 2-dimensional harmonic oscillator plus a free particle. It is also shown that the eigenvectors of the discrete spectrum are entangled states of the 2-dimensional harmonic oscillator.

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