  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.
