Short note: Hamiltonian for a particle with position-dependent mass

Manuel Gadella, Oleg Georgievich Smolyanov

Shi‐Hai Dong

Yamen Hamdouni

These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with arbitrary ordering ambiguity parameters, and a simple scheme to convert the problem to a constant-mass motion is presented. The motion in curved spaces is treated along the same lines, where a phase space formulation is used to derive the propagator for arbitrary discretization choices.

Anderson L. de Jesus, Alexandre G. M. Schmidt

Abstract The purpose of this work is to reproduce the dynamic of a neutral quantum particle bounded in a conical surface utilizing a position-dependent effective mass background in the non-relativistic regime. We start this task with the construction of the position-dependent effective mass Hamiltonian, containing the effective potential in the Zhou–Kroemer parametrization. We obtain a differential equation for the mass distribution which could reproduce the exact wavefunctions of a scalar quantum particle constrained to a conical space.

I. M. Benn, R.W. Tucker

Nedjma Bouchemla, L. Chétouani