Eigenfunctions and eigenvalues of the Thomas-Fermi density matrix. The simple harmonic oscillator
- 1 April 1973
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 58 (7), 2813-2820
- https://doi.org/10.1063/1.1679583
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.Keywords
This publication has 10 references indexed in Scilit:
- Exponential Hamiltonian: Convergence in an iterated product representation for a linear harmonic oscillatorThe Journal of Chemical Physics, 1973
- Continuous Representations in the Statistical Theory of Electronic Energies. The H2+ IonThe Journal of Chemical Physics, 1966
- Analysis of the Statistical Density MatrixPhysical Review B, 1961
- Statistical Theory of Electronic EnergiesReviews of Modern Physics, 1960
- Spherical Eigenfunctions and Angular Momentum Distributions in the Statistical Theory of AtomsPhysical Review B, 1958
- Statistical Theory of Many-Electron Systems. Discrete Bases of RepresentationPhysical Review B, 1957
- Statistical Theory of Many-Electron Systems. General Considerations Pertaining to the Thomas-Fermi TheoryPhysical Review B, 1957
- The Thomas-Fermi approximation in quantum mechanicsAdvances in Physics, 1957
- Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der ElementeThe European Physical Journal A, 1928
- The calculation of atomic fieldsMathematical Proceedings of the Cambridge Philosophical Society, 1927