Quasiperiodic quantum states

Abstract

We show that the Hose–Taylor criterion of quantum quasiperiodicity can be recovered from low‐order nondegenerate perturbation theory. It is seen that this mnemonic, which purports to identify energy levels which can be obtained by quantizing classical quasiperiodic motions, can lead to contradictions when applied to systems which are more semiclassical than that treated previously. These discrepancies arise since the criterion is both perturbation scheme and basis set dependent: the correlation between the semiclassical quantization and such a definition of quantum quasiperiodic behavior is not straightforward. As the underlying search is for a quantum KAM‐like theory (in particular for near‐separable systems which are typical of molecular vibrational Hamiltonians) some possibilities are discussed.