Unacceptable kinetic energy operators in effective-mass Hamiltonians for graded mixed crystals

Abstract
A previous study of a class of Hermitian Hamiltonians with position-dependent effective mass for graded mixed crystals is generalized. Before, we considered only abrupt heterojunctions. Now, we relax that restriction and suggest a criterion for rejecting certain kinetic energy operators in one, two, and three spatial dimensions for any form of grading.