Semiclassical density of states in a central potential
= Semiclassical density of states in a central potential
For a spinless nonrelativistic particle in a central potential, $g(\epsilon)=(2m)^{3/2}(4\pi^2\hbar^3)^{-1}\int_{U<\epsilon}\sqrt{\epsilon-U}\,d^3r$. Spherical symmetry reduces this to a radial integral over every allowed shell. It is a leading phase-space approximation.