Rw. Robinett, ENERGY EIGENVALUES AND PERIODIC-ORBITS FOR THE CIRCULAR DISK OR ANNULAR INFINITE WELL, Surface review and letters, 5(2), 1998, pp. 519-526
We compute the Fourier transform [rho(L)] of the quantum-mechanical en
ergy level density for the problem of a particle in an annular infinit
e well (or circular disk) of outer (inner) radius R-max = R (R-min = f
R). For various values of f = R-min/R we then explicitly compare rho(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 tha
t at least one recurrence of that feature is present in the spectrum,
and discussing the corresponding effective path lengths for these feat
ures.