Abstract
In previous papers [Uwano, 1994, 1995], it was shown that a degeneracy of energy levels is a quantum counterpart of a Hamiltonian pitchfork bifurcation of periodic trajectories of a certain 1:1 resonant oscillator with two parameters. As a continuation of those papers, a quantum study is made from a geometric point of view in order to find a quantum counterpart of a saddle-node bifurcation taking place in a certain 1:1 resonant perturbed oscillator with three parameters. The torus quantization method is applied to the perturbed oscillator to show that a degeneracy of energy levels is a quantum counterpart of that bifurcation: The bifurcation set for the saddle-node bifurcation in classical theory is viewed as a "bifurcation set" for the degeneracy of energy levels in quantum theory.
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