Deformed Quantum Mechanics and the Landau Problem

Abstract

A deformation of the Landau problem based on a modification of Fock algebra is considered. Systems with the Hamiltonians f ( Ĥ) where Ĥ is the Landau Hamiltonian in the lowest level are discussed. The case f ( Ĥ) = α1 Ĥ + α2 Ĥ2 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.