Canonical transformations applied to the non-free Landau electron

TL;DR

This paper applies canonical transformations to derive and interpret the wave function of a non-free Landau electron, providing insights into its physical properties under a magnetic field.

Contribution

It extends previous methods by using canonical transformations to analyze the Landau electron, offering a new perspective on its wave function and conserved properties.

Findings

Derived the wave function for a non-free Landau electron.

Provided physical interpretation based on conserved Hamiltonian properties.

Demonstrated the applicability of canonical transformations in this context.

Abstract

The method previously used to solve Schr\"odinger 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.