Operator ordering in effective-mass theory
J. Thomsen;G.T. Einevoll; P.C. Hemmer,
Institutt for Fysikk, Norges Teknisk Høgskole,
Universitetet i Trondheim, 7034 Trondheim, Norway
Physical Review B 39, 12783-12788 (1989)
Abstract
The authors study the problem of operator ordering in the
effective-mass Hamiltonian with kinetic energy operator 1/4 (m^{\alpha}
p m^{\beta} p m^{\gamma} + m^{\gamma} p m^{\beta} p m^{\alpha}),
for a position-dependent effective mass m. Here \alpha + \beta + \gamma =-1.
They use merely the inherent criterion that the eigenvalues of the
Hamiltonian should correspond to finite and uniquely determined energies.
Through exact model calculations they show first that divergences occur
unless \alpha = \gamma , and second that \alpha = \gamma =0, \beta =-1 is the
only universal set of operator ordering parameters which gives unique
results.