Abstract
Attention is focussed here on a variety of cylindrically symmetric inhomogeneous electron liquids. These include separable potentials in which a general variation along the (z) axis of cylindrical symmetry is combined with isotropic harmonic confinement in the (x, y) plane. in this case, an explicit differential equation is derived for the Slater sum along the z axis by projecting out of the (off-diagonal) canonical density matrix the states with zero angular momentum about the axis of symmetry. Some attention is then given to the calculation of the Slater sum for a hydrogen-like atom in a uniform electric field of arbitrary strength. the model of a separable potential with harmonic confinement, though no longer exact, is shown to lead directly to a (now approximate) equation for the Slater sum along the z axis for the Stark effect in hydrogen. Finally some further progress is shown to be possible in the extreme high field limit.
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