Operator ordering in effective-mass theory for heterostructures.
I. Comparison with exact results for superlattices, quantum wells, and
localized potentials.
G.T. Einevoll; P.C. Hemmer; J. Thomsen ,
Institutt for Fysikk, Norges Teknisk Høgskole,
Universitetet i Trondheim, 7034 Trondheim, Norway
Physical Review B 42, 3485-3496 (1990)
Abstract
The authors study, for heterostructures with abrupt interfaces, the
problem of operator ordering in the effective-mass Hamiltonian with
kinetic-energy operator 1/2 m^{\alpha} p m^{\beta} p m^{\alpha}, for a
position-dependent effective mass. Here, 2 \alpha + \beta =-1. Through exact
model calculations on superlattices, quantum wells, and localized
potentials they show that when effective-mass theory is applicable, \alpha
=0 and \beta =-1. In all cases the effective-mass theory has the status of
an asymptotically exact treatment, except for strained lattices.