Application of the Kohn variational principle to a particle of effective mass m*

Abstract

The original Kohn variational principle (1948) was based upon the stationarity of L-4 pi ka where L= integral psi (H-E) psi d tau . Here, it is pointed out that this must be modified for a calculation in atomic units involving a particle of effective mass m*. The appropriate stationary quantity becomes L-4 pi ka/2 alpha 0 where alpha 0=m*/m (m*=effective mass, m=electron mass). The author comments upon a recent calculation by Mohammad (1979) which fails to use this modification. The problem is of interest in the study of ionised impurity scattering in semiconductors.