Slater sum for a three-dimensional inhomogeneous Fermi fluid with one-dimensional harmonic confinement
Faculty of Sciences. Physics
Physics and chemistry of liquids. - London
, p. 173-179
In early work, Bardeen  proposed a model whereby a three-dimensional Fermi fluid is confined to a half-space by a planar infinite barrier in the xy plane. Brown, Brown and March  subsequently worked out the Slater sum S(z, beta), beta = 1/k(B)T, for this same model of partial confinement. The present work considers S(z, beta) for additional harmonic confinement in the z direction. When the harmonic force constant is switched off the Slater sum calculated by Brown, Brown and March is recovered. The off-diagonal Slater sum, namely the canonical density matrix, is treated which in turn yields the Feynman propagator for this model when the reciprocal temperature beta is replaced by the pure imaginary time.