OPERATOR ORDERING IN EFFECTIVE-MASS THEORY FOR HETEROSTRUCTURES .1. COMPARISON WITH EXACT RESULTS FOR SUPERLATTICES, QUANTUM-WELLS, AND LOCALIZED POTENTIALS

We study, for heterostructures with abrupt interfaces, the problem of operator ordering in the effective-mass Hamiltonian with kinetic-energy operator 1/2mpmpm, for a position-dependent effective mass. Here, 2+=-1. Through exact model calculations on superlattices, quantum wells, and localized potentials we show that when effective-mass theory is applicable, =0 and =-1. In all cases the effective-mass theory has the status of an asymptotically exact treatment, except for strained lattices. © 1990 The American Physical Society.