Effective Hamiltonian for piecewise flat potentials and masses

Abstract

We consider a class of Hermitian Hamiltonians with position-dependent mass $H=((m^alpha)p(m^beta)p(m^alpha))/2+\V$ with $2(alpha)+\beta=-1$. We apply these Hamiltonians to different piecewise flat potentials and masses (step, barrier, well and multibarrier). To raise the ordering ambiguity we impose that the transmission coefficient tends to the unity as the energy increases indefinitely. We arrive at the conclusion that the form $H_flat=(m^(-1/4)pm^(-1/2)pm^(-1/4))/2+\V$ of the effective Hamiltonian is the most adequate to describe such flat potentials and masses systems.