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

• Received 12 July 2006
• Publisher error corrected 20 February 2007

DOI:https://doi.org/10.1103/PhysRevA.74.053624