Geodesic
An integral semiclassical method for calculating the spectra for centrally symmetric potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 463-480
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We develop a new approach to semiclassical quantization conditions that does not involve asymptotic expansions and is based on exact general properties of wave equations and their spectra. For centrally symmetric potentials, the quantization conditions depend only on a collection of integrals involving powers of the classical momentum. The energy levels calculated using these conditions are in good agreement with numerical data. 
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A. A. Lobashev; N. N. Trunov. An integral semiclassical method for calculating the spectra for centrally symmetric potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 463-480. http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a7/

[1] A. A. Lobashev, N. N. Trunov, TMF, 120 (1999), 99 | DOI | MR | Zbl

[2] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 4. Analiz operatorov, Mir, M., 1982 | MR | Zbl

[3] C. Quigg, J. L. Rosner, Phys. Rep., 56 (1979), 167 | DOI | MR

[4] P. V. Elyutin, V. D. Krivchenkov, Kvantovaya mekhanika s zadachami, Nauka, M., 1976

[5] A. B. Migdal, Kachestvennye metody kvantovoi teorii, Nauka, M., 1974 | MR

[6] B. M. Karnakov, V. D. Mur, V. S. Popov, ZhETF, 107 (1995), 1768

[7] A. A. Lokshin, E. A. Sagomonyan, Geometricheskie metody v teorii spektrov, Izd-vo MGU, M., 1996 | Zbl

[8] Yu. V. Tarbeev, N. N. Trunov, A. A. Lobashev, V. V. Kukhar, ZhETF, 112 (1997), 1226

[9] Z. Flyugge, Zadachi po kvantovoi mekhanike, T. 1, Mir, M., 1974, s. 187

[10] M. V. Fedoryuk, Asimptotika: integraly i ryady, Nauka, M., 1987 | MR

[11] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza, Ch. II, Fizmatgiz, M., 1963

[12] V. M. Mostepanenko, N. N. Trunov, Effekt Kazimira i ego prilozheniya, Energoatomizdat, M., 1990

[13] O. I. Marichev, Metod vychisleniya integralov ot spetsialnykh funktsii (teoriya i tablitsy formul), Nauka i tekhnika, Minsk, 1978 | MR