rnThat the bound energy eigenstates of one-dimensional quantum systems can 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 singularity in the potential and the importance of tunneling is highlighted in this context to analyze the general nature of such potentials leading to double degeneracy. Additionally, the case of spiked oscillators is discussed with particular reference to the "Klauder phenomenon," revealing clearly that the mere presence of singularity in the potential is not a sufficient criterion for the occurrence of degeneracy. 0 1996 John Wiley

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mA recipe for the accurate calculation of eigenstates of quartic double-well oscillators is presented. The behavior of eigenenergies as a function of the coupling strength is also studied. The quality of the semiclassical (WKB) expression for eigenvalues is critically assessed in this context. The analysis also includes a discussion on the possibility of degeneracy in such one-dimensional systems. 0

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