Tomographic probability representation in the problem of transitions between the Landau levels

TL;DR

This paper employs tomographic probability representation to analyze transitions between Landau levels of a charged particle in a magnetic field, providing a probabilistic approach to quantum state transitions.

Contribution

It introduces a method to calculate Landau level transition probabilities using symplectic tomograms instead of traditional wave functions.

Findings

Transition probabilities are derived from tomograms, not wave functions.

The method applies to varying electromagnetic fields.

Results generalize previous static field analyses.

Abstract

The problem of moving of a charged particle in electromagnetic field is considered in terms of tomographic probability representation. The coherent and Fock states of a charge moving in varying homogeneous magnetic field are studied in the tomographic probability representation of quantum mechanics. The states are expressed in terms of quantum tomograms. The Fock state tomograms are given in the form of probability distributions described by multivariable Hermite polynomials with time-dependent arguments. The obtained results are generalized in the present work and are applied to determining the transition probabilities between Landau levels. Transition probabilities are calculated using the symplectic tomograms instead of the wave functions. The same method is used in obtaining the transition probabilities between the Landau levels possessed by a charge moving in varying electromagnetic field.