Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2000-10-15
Phys. Rev. Lett. 86, 1574 (2001)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
4 pages, 4 figures; corrected version
Scientific paper
10.1103/PhysRevLett.86.1574
We derive simple analytical expressions for the particle density $\rho(r)$ and the kinetic energy density $\tau(r)$ for a system of noninteracting fermions in a $d-$dimensional isotropic harmonic oscillator potential. We test the Thomas-Fermi (TF, or local-density) approximation for the functional relation $\tau[\rho]$ using the exact $\rho(r)$ and show that it locally reproduces the exact kinetic energy density $\tau(r)$, {\it including the shell oscillations,} surprisingly well everywhere except near the classical turning point. For the special case of two dimensions (2D), we obtain the unexpected analytical result that the integral of $\tau_{TF}[\rho(r)]$ yields the {\it exact} total kinetic energy.
Brack Matthias
van Zyl Brandon P.
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