Abstract
We consider a class of potentials for which the exact semiclassical quantization is achieved by a certain modification of the quantization condition. A list of potentials for which the new quantization condition is exact coincides with the list of potentials for which the spectrum is determined by the factorization method. We construct a one-parameter family of quantization conditions including the supersymmetric WKB condition as a special case. The new condition allows considering the interrelations between different modifications of the leading approximation and their validity ranges and also allows developing new approximate methods for calculating spectra.
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Trunov, N.N. A Class of Potentials for Which Exact Semiclassical Quantization Can Be Achieved. Theoretical and Mathematical Physics 138, 407–417 (2004). https://doi.org/10.1023/B:TAMP.0000018456.68244.21
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DOI: https://doi.org/10.1023/B:TAMP.0000018456.68244.21