The quantum-mechanical solution for the biharmonic oscillator is presented. This one-dimensional asymmetric oscillator is described by the potential energy function V(x) = mω12x2/2, x ≳ 0, and V(x) = mω22x2/2, x < 0. One of the more interesting features of the solution is that the energy levels are very nearly equally spaced. The biharmonic oscillator provides a relatively simple model for systems which lack the symmetry of the harmonic oscillator.
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Gettys et al. (1975) studied this question.