Energy eigenvalues and periodic orbits for the circular disk or annular infinite well

We compute the Fourier transform [ρ(L)] of the quantum-mechanical energy level density for the problem of a particle in an annular infinite well (or circular disk) of outer (inner) radius R_max = R (R_min = f R). For various values of f = R_mim/R we then explicitly compare ρ(L) to the lengths of the classical periodic orbits. We also comment on the diffraction peak seen by Reimann et al. in this system, noting that at least one recurrence of that feature is present in the spectrum, and discussing the corresponding effective path lengths for these features.