Abstract
We study, for heterostructures with abrupt interfaces, the problem of operator ordering in the effective-mass Hamiltonian with kinetic-energy operator 1/2pp, for a position-dependent effective mass. Here, 2α+β=-1. Through exact model calculations on superlattices, quantum wells, and localized potentials we show that when effective-mass theory is applicable, α=0 and β=-1. In all cases the effective-mass theory has the status of an asymptotically exact treatment, except for strained lattices.
- Received 9 February 1990
DOI:https://doi.org/10.1103/PhysRevB.42.3485
©1990 American Physical Society