DEGENERACY IN ONE-DIMENSION - ROLE OF SINGULAR POTENTIALS

That the bound energy eigenstates of one-dimensional quantum systems c an be degenerate in the presence of specific singular or supersingular potentials is demonstrated by choosing a family of bistable and other oscillators. Relevance of our study to spectroscopic observations is noted. Quasi-degeneracy is found even in the absence of any singularit y in the potential and the importance of tunneling is highlighted in t his context to analyze the general nature of such potentials leading t o double degeneracy. Additionally, the case of spiked oscillators is d iscussed with particular reference to the ''Klauder phenomenon,'' reve aling clearly that the mere presence of singularity in the potential i s not a sufficient criterion for the occurrence of degeneracy. (C) 199 6 John Wiley & Sons, Inc.