Deformed Quantum Mechanics and the Landau Problem

TL;DR

This paper introduces a deformation of the Landau problem through modified Fock algebra, enabling exact solutions for new Landau-like systems and connecting parameters to experimental data like the Zeeman effect.

Contribution

It presents a novel deformation approach to the Landau problem that allows exact solutions for a broader class of Hamiltonians, linking theoretical parameters to experimental measurements.

Findings

Exact solutions for deformed Landau systems are obtained.

Parameters can be fixed using Zeeman effect data.

New solvable Landau-like problems are identified.

Abstract

A deformation of the Landau problem based on a modification of Fock algebra is considered. Systems with Hamiltonians f(H) where H is the Landau Hamiltonian in the lowest level are discussed. The case $f(H) = {\alpha} H + b H^2$ is studied and it is shown that in this particular example, parameters of the problem can be fixed by using the quadratic Zeeman effect data and the Breit- Rabi formula. The proposed approach allows to solve exactly Landau-like families of problems not previously discussed in the literature.