Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions

Details Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions

2006-07-13

arxiv.org/abs/cond-mat/0607340v1

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

10.1103/PhysRevA.74.053624

We present a unique theoretical description of the physics of the spherically trapped $N$-atom degenerate Fermi gas (DFG) at zero temperature based on an ordinary Schr\"{o}dinger equation with a microscopic, two body interaction potential. With a careful choice of coordinates and a variational wavefunction, the many body Schr\"{o}dinger equation can be accurately described by a \emph{linear}, one dimensional effective Schr\"{o}dinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius and peak density of ground state energy are made to those predicted by Hartree-Fock (HF). Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.

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