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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] F. Cooper, A. Khare, U. Sukhatme, Phys. Rep., 251 (1995), 267 ; E-print hep-th/9405029 | DOI | MR

[2] M. Hrŭska, W. Y. Keung, U. Sukhatme, Phys. Rev. A, 55 (1997), 3345 | DOI | MR

[3] V. M. Galitskii, B. M. Karnakov, V. I. Kogan, Zadachi po kvantovoi mekhanike, Nauka, M., 1992 | MR

[4] M. Friedrich, J. Trost, Phys. Rev. A, 54 (1996), 1136 | DOI | MR

[5] R. A. Leacock, M. J. Padgett, Phys. Rev. D, 28 (1983), 2491 | DOI | MR

[6] J. Hainz, H. Grabert, Phys. Rev. A, 60 (1999), 1698 | DOI

[7] S. Yu. Slavyanov, Asimptotika reshenii odnomernogo uravneniya Shredingera, Izd-vo LGU, L., 1990 | MR

[8] A. F. Nikiforov, V. B. Uvarov, Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1984 | MR

[9] L. Infeld, T. E. Hull, Rev. Mod. Phys., 32:1 (1951), 21 | DOI | MR

[10] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika. Teoreticheskaya fizika, T. 3, Nauka, M., 1988 | MR

[11] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[12] A. D. Sukhanov, TMF, 132:3 (2002), 449 | DOI | MR | Zbl

[13] P. Holland, The Quantum Theory of Motion, Cambridge Univ. Press, Cambridge, 1993 | MR

[14] M. V. Fedoryuk, Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983 | MR | Zbl

[15] K. S. Mamaeva, N. N. Trunov, TMF, 135:1 (2003), 82 | DOI | MR | Zbl

[16] A. A. Lobashev, N. N. Trunov, TMF, 120:1 (1999), 99 ; 124:3 (2000), 463 | DOI | MR | Zbl | DOI | MR | Zbl

[17] Yu. V. Tarbeyev, N. N. Trunov, A. A. Lobashev, V. V. Kukhar, “Effective quantum number of centrally symmetric potentials”, Operator Methods in Ordinary and Partial Differential Equations, Proc. of the Sonja Kovalevsky Symp. (Stockholm, June 16–22, 2000), Operator Theory: Advances and Applications, 132, eds. S. Albeverio, N. Elander, W. N. Everitt, P. Kurasov, Birkhäuser, Basel, 2002, 403 | MR | Zbl

[18] A. I. Baz, Ya. B. Zeldovich, A. M. Perelomov, Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, Nauka, M., 1971 | Zbl

[19] Kh. Grin, Matrichnaya kvantovaya mekhanika, Mir, M., 1968 | MR