A Hyperspherical Variational Approach to the N-Fermion Problem

摘要

A variational treatment in hyperspherical coordinates is developed to describe the two-component normal Fermi gas with two-body zero-range interactions. We adopt a variational trial function that is a Slater determinant of noninteracting oscillator functions, multiplied by an unspecified function of the hyperradius. Optimization of the hyperradial function approximately reduces the many-body problem to a linear, one-dimensional Schrödinger equation in the hyperradius R of the N-atom system. Results from this variational treatment are compared with more conventional descriptions based on mean-field theory.