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Feynman integral treatment of the Bargmann potential. (English) Zbl 1139.81366

Summary: A method based on path integral formulation is given for obtaining exact solution of the \(s\) states for the Bargmann potential \(V(r)\). The exact energy spectrum and the normalised \(s\)-state eigenfunctions are obtained from the poles of the Green function and their residues, respectively. The results are compared with their of Schrödinger formalism, special cases are also discussed.

MSC:

81S40 Path integrals in quantum mechanics
81U05 \(2\)-body potential quantum scattering theory
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[1] Shifman, M. A., Int. J. Mod. Phys. A, 4, 2897 (1989)
[2] Dutt, R.; Khare, A.; Varshni, Y. P., J. Phys. A, 28, L107 (1995)
[3] Feynman, R. P.; Hibbs, Quantum Mechanics and Path Integrals (1965), McGraw-Hill: McGraw-Hill New York · Zbl 0176.54902
[4] Khandekar, D. C.; Lawande, S. V.; Bhagmat, K. V., Path Integral Methods and their Applications (1986), World Scientific: World Scientific Singapore
[5] Duru, I. H.; Kleinert, H., Phys. Lett. B, 84, 185 (1979)
[6] Groshe, C.; Steiner, F., Handbook of Feynman Path Integrals (1998), Springer: Springer Berlin · Zbl 1029.81045
[7] Cai, J.; Cai, P.; Inomata, A., Phys. Rev. A, 34, 6, 4621 (1986)
[8] Chetouani, L.; Chouchaoui, A.; Hamann, T. F., J. Math. Phys., 31, 983 (1990)
[9] Manning, M. F., Phys. Rev., 44, 951 (1933)
[10] Chetouani, L.; Guechi, L.; Letlout, M.; Hamann, T. F., Nuovo Cimento B, 105, 387 (1990)
[11] Cai, P. Y.; Inomata, A.; Wilson, R., Phys. Rev. Lett. A, 96, 117 (1983)
[12] Inomata, A.; Kayed, M. A., Phys. Lett. A, 108, 9 (1985)
[13] Inomata, A.; Kayed, M. A., J. Phys. A, 18, L235 (1985)
[14] Schulman, L. S., Techniques and Applications of Path Integration (1981), Wiley: Wiley NewYork · Zbl 0587.28010
[15] Frank, A.; Woff, K. B., Phys. Rev. Lett., 52, 1735 (1984)
[16] Inomata, V. A.; Kuratsuji, H.; Gerry, C. C., Path Integrals and Coherent States of SU(2) and SU(1,1) (1992), World Scientific: World Scientific Singapore
[17] Junker, G.; Inomata, A., Path Integrals on \(S^3\) and its applications to the Rosen-Morse Oscillator, Path integrals From mev to Mev (1989), World Scientific: World Scientific Singapore
[18] Vilinkin, N. J., Special Functions and the Theory of Group Representation (1968), American Mathematical Society: American Mathematical Society Providence, Rhode Island, p. 130
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