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On a new technique to manufacture isochronous Hamiltonian systems: classical and quantal treatments

Abstract We discuss a new technique to ω-modify real Hamiltonians so that they become isochronous while remaining real. Although the ω-modified Hamiltonians thereby obtained often yield, in the classical context, singular motions, we exhibit and investigate simple examples when this does not (quite) happen. We also identify quantized versions of some of these isochronous models featuring equispaced spectra, and observe that there are cases when in the classical context the motions run into singularities while in the quantal context it is nevertheless justified to arrive at nonsingular models with equispaced spectra.