Semiclassical treatment of bound state systems. II. Trajectory calculations using the exact quantum momentum

Abstract

Equations of motion based upon the exact solution of the Milne equation are used to perform trajectory calculations. Using the trajectory information we calculate charge densities for N fermions in a harmonic oscillator potential in a semiclassical approximation. The charge densities so obtained are in almost exact agreement with exact calculation within the outermost density maxima. Outside this region the differences between the approximate and exact densities are essentially independent of the number of fermions in the system.