Two-dimensional position-dependent massive particles in the presence of magnetic fields

Abstract

In this work, we discuss the problem of a particle with a position-dependent mass interacting with a two-dimensional potential well with finite depth, as well as under the influence of a uniform magnetic field. The ordering ambiguity is taken in account, and we obtain the exact wavefunctions and energies for a complete set of eigenstates. It is shown that, even considering a finite-depth potential well, the system retains an infinite set of quantum states.