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arXiv:2405.09706

Canonical transformations applied to the non-free Landau electron

Jorge A. Lizarraga

Published May 15, 2024• 0 citations
arXivHTMLPDF

Abstract

The method previously used to solve Schrödinger equation by a unitary transformation for a electron under the influence of a constant magnetic field is used to obtain a non-free Landau electron wave function. The physical meaning of this wave function is discussed based on the conserved properties of the transformed Hamiltonian.
DOI
10.48550/arxiv.2405.09706

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It is shown that the problem of a free eletron in a uniform magnetic field provides an interesting example for the use of recently developed canonical transformation methods in quantum mechanics. The Schrödinger equation is immediately solved by a unitary transformation corresponding to a finite linear symplectic transformation in phase space. The natural invariance and dynamical groups involve affine and not only linear symplectic transformations, and the Weyl group turns out to be an appropriate invariance group to account completely for the infinite degeneracies.
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