Geodesic
Singular center as a nongravitational black hole
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 603-613 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the interpretation of a singular center in quantum mechanics as a black hole in application to the exactly solvable problem of the three-dimensional oscillator with a complex-valued angular momentum, also known as the generalized Calogero problem.
Keywords: singular potential, fall to the center, quantum mechanical black hole. 
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A. E. Shabad. Singular center as a nongravitational black hole. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 603-613. http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a12/

[1] G. 't Hooft, Nucl. Phys. B, 35:1 (1971), 167–188 | DOI

[2] W. Heisenberg, Z. Physik, 101:9–10 (1936), 533–540 ; A. T. Filippov, Phys. Lett., 9:1 (1964), 78–80 ; W. Güttinger, R. Penzl, E. Pfaffelhuber, Ann. Phys. (N. Y.), 33:2 (1965), 246–271 | DOI | DOI | MR | DOI | MR

[3] A. A. Slavnov, A. E. Shabad, YaF, 1 (1965), 721–728

[4] G. Feinberg, A. Pais, Phys. Rev. B, 133:2B (1964), B477–B486 | DOI | MR

[5] A. E. Shabad, Singular centre in quantum mechanics as a black hole, arXiv: ; A. E. Shabad, “Black-hole approach to the singular problem of quantum mechanics”, Proceedings of the 3rd International Sakharov Conference on Physics (Moscow, Russia, June 24 – 29, 2002), 1, eds. A. Semikhatov, M. Vasiliev, V. Zaikin, World Sci., Singapore, 2003, 817–826 hep-th/0208133

[6] A. E. Shabad, Black-hole approach to the singular problem of quantum mechanics. II, arXiv: hep-th/0403177

[7] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Nauka, M., 1989 | MR | Zbl

[8] A. E. Shabad, J. Phys. A: Math. Gen., 38:33 (2005), 7419–7439, arXiv: hep-th/0502139 | DOI | MR

[9] K. M. Case, Phys. Rev., 80:5 (1950), 797–806 | DOI | MR | Zbl

[10] K. Meetz, Nuovo Cimento, 34 (1964), 690–708 | DOI | MR | Zbl

[11] F. M. Mors, G. Feshbakh, Metody teoreticheskoi fiziki, v. 2, IL, M., 1960 ; М. Рид, Б. Саймон, Методы современной математической физики, т. 2, Гармонический анализ. Самосопряженность, Мир, М., 1978 | MR | Zbl | MR

[12] D. M. Gitman, I. V. Tyutin, B. L. Voronov, Self-Adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials, Progress in Mathematical Physics, 62, Birkhäuser, New York, 2012 | MR | Zbl

[13] F. Calogero, J. Math. Phys., 12:3 (1971), 419–436 | DOI | MR

[14] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979 | MR | MR | Zbl

[15] I. V. Tyutin, chastnoe soobschenie

[16] I. V. Tyutin, B. L. Voronov, Phys. Scr., 87:3 (2013), 038119, 14 pp., arXiv: ; D. M. Gitman, I. V. Tyutin, B. L. Voronov, J. Phys. A: Math. Theor., 44:42 (2011), 425204, 17 pp., arXiv: 1211.63310907.1736 | DOI | MR | Zbl | DOI | MR | Zbl

[17] E. Kamke, Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971 | MR | Zbl

[18] L. D. Landau, E. M. Lifshits, Mekhanika, Nauka, M., 1988 | MR