Geodesic
The stationary perturbation theory in case of a potential-series
Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 29-35.

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The procedure for constructing of stationary perturbation theory for the Schrodinger equation and corrections to the energy spectrum and corresponding wave functions is implemented in case of the potential, represented in the form of a series in powers of a small parameter (potential-series). The application of the obtained scheme for the anharmonic oscillator is examined as a physical example.
Keywords: stationary perturbation theory, Schrödinger equation, wave function, energy spectrum, potential, anharmonic oscillator.
Mots-clés : correction 
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V. N. Kapshai; L. D. Korsun. The stationary perturbation theory in case of a potential-series. Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 29-35. http://geodesic.mathdoc.fr/item/PFMT_2011_1_a3/

[1] A. Messia, Kvantovaya mekhanika, v. 1, Nauka, M., 1978 | MR

[2] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972

[3] Dzh. D. Berken, S. D. Drell, Relyativistskaya kvantovaya teoriya, v. 1, Mir, M., 1978

[4] K. Itsikson, Zh.-B. Zyuber, Kvantovaya teoriya polya, v. 1, 2, Mir, M., 1984

[5] Tyuterev Vl. G., “Effektivnye gamiltoniany”, Vnutrimolekulyarnye vzaimodeistviya i infrakrasnye spektry atmosfernykh gazov, Tomsk, 1975, 3–46

[6] V. S. Polikanov, “K nerelyativistskoi teorii vozmuschenii dlya diskretnogo spektra”, ZhETF, 52:5 (1967), 1326

[7] A. V. Turbiner, “Zadacha o spektre v kvantovoi mekhanike i protsedura «nelinearizatsii»”, UFN, 144:1 (1984), 35 | DOI | MR

[8] S. P. Alliluev i dr., “Logarifmicheskaya teoriya vozmuschenii i ee primenenie k effektu shtarka v atome vodoroda”, ZhETF, 82:1 (1982), 77

[9] W. N. Mei, D. S. Chuu, “Higher-order corrections to the excited states using the logarithmic perturbation method”, Phys. Rev. A, 58:1 (1998), 713 | DOI

[10] Y. Aharonov, C. K. Au, “A New Approach to Perturbation Theory”, Phys. Rev. Lett., 42 (1979), 1582 | DOI

[11] S.-A. Yahiaoui, O. Cherroud, M. Bentaiba, “The effective potential and resummation procedure to multidimensional complex cubic potentials for weak and strong-coupling”, J. Math. Phys., 48 (2007), 113503 | DOI | MR

[12] I. L. Solovtsov, “New expansion in QCD”, Phys. Lett. B, 327 (1994), 335 | DOI

[13] L. D. Korsun, A. N. Sissakian, I. L. Solovtsov, “Variational perturbation theory: the $\varphi^{2k}$-oscillator”, Teor. Mat. Fiz., 90 (1992), 37–54 | DOI | MR

[14] L. D. Korsun, A. N. Sissakian, I. L. Solovtsov, “$\varphi^{2k}$-oscillator in the strong coupling limit”, Int. J. Mod. Phys. A, 8 (1993), 5129–5140 | DOI

[15] A. A. Logunov, A. N. Tavkhelidze, “Quasi-optical approach in quantum field theory”, Nuovo Cimento, 29 (1963), 380–399 | DOI | MR

[16] V. G. Kadyshevsky, “Quasipotential type equation for the relativistic scattering amplitude”, Nucl. Phys. B, 6:1 (1968), 125–148 | DOI

[17] A. A. Sokolov, I. M. Ternov, V. Ch. Zhukovskii, Kvantovaya mekhanika, Nauka, M., 1979