Eigenfunctions and eigenvalues of the Thomas-Fermi density matrix. The simple harmonic oscillator

Abstract
The eigenfunctions and eigenvalues of a Hermitian Thomas‐Fermi density matrix for the one‐dimensional harmonic oscillator are examined in detail. The major defect of Thomas‐Fermi theory is shown to be the departure of the density matrix from N representability. The imposition of indempotency leads to greatly improved particle densities, including very well developed density oscillations.