Geodesic
A~Class of Potentials for Which Exact Semiclassical Quantization Can Be Achieved
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 480-490

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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.
Keywords: semiclassical approximation, method for the Hamiltonian factorization, supersymmetry in quantum mechanics. 
@article{TMF_2004_138_3_a9,
     author = {N. N. Trunov},
     title = {A~Class of {Potentials} for {Which} {Exact} {Semiclassical} {Quantization} {Can} {Be} {Achieved}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {480--490},
     publisher = {mathdoc},
     volume = {138},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a9/}
}
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N. N. Trunov. A~Class of Potentials for Which Exact Semiclassical Quantization Can Be Achieved. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 480-490. http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a9/