  In this paper, the quantum spectrum of isochronous potentials is
investigated. Given that the frequency of the classical motion in such
potentials is energy-independent, it is natural to expect their quantum spectra
to be equispaced. However, as it has already been shown in some specific
examples, this property is not always true. To gain some general insight into
this problem, a WKB analysis of the spectrum, valid for any analytic potential,
is performed and the first semiclassical corrections to its regular spacing are
calculated. We illustrate the results on the two-parameter family of
isochronous potentials derived in [1], which includes the harmonic oscillator,
the asymmetric parabolic well, the radial harmonic oscillator and Urabe's
potential as special limiting cases. In addition, some new analytical
expressions for families of isochronous potentials and their corresponding
spectra are derived by means of the above-mentioned method.
