On a class of Hamiltonians with (classical) isochronous motions and (quantal) equi-spaced spectra

Hamiltonians linear in the momenta and yielding (in the classical context) trajectories isochronous in configuration space are considered. It is shown that their motions are completely periodic in phase space as well, with the same common period as the orbits in configuration space. Moreover, it is shown that for this particular class of Hamiltonians the semiclassical quantization prescription is exact, so that to the isochronous character of their classical dynamics there corresponds in the quantized context an equidistant spectrum, for a broad range of ordering prescriptions, including non-symmetrical ones. Examples illustrating these findings are presented.