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Acta Physica Polonica A

Closed Relation Between Single-Particle Kinetic Energy and Electron Density in One-Dimensional Two-Level Systems

Pawel Michal Kozlowski, Norman Henry March

Published Sep 1, 1992• 0 citations
Publisher

Abstract

For a two-level problem in one dimension, an implicit relation is derived relating the kinetic energy density t s (x) to the electron density p(x) plus its first and second derivatives.As an example, tle harmonic oscillator potential is used to make this relation explicit.
DOI
10.12693/aphyspola.82.421

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Using the known perturbation series for the idempotent Dirac density matrix in powers of a given one-body potential V(r)V(\mathbf{r})V(r), Stoddart and March (SM) generated a corresponding series for the kinetic energy density. While the general term of the SM series is known, a summation has not been achieved to date. A contribution to solve this problem is made here by exhibiting an explicit form of the above kinetic energy density for Fermions filling an arbitrary number of closed shells, when the confinement is harmonic. This example is of considerable current interest because of ongoing experiments on ultracold atomic gases of Fermions.