Deformed Quantum Mechanics and the Landau Problem

A deformation of the Landau problem based on a modification of Fock algebra is considered. Systems with the Hamiltonians f(A) where Ais the Landau Hamiltonian in the lowest level are discussed. The case f(A) = 1A+ α2A2 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. © 2021 World Scientific Publishing Company.