Geodesic
Jacobi algebra and potentials generated by it
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the Jacobi algebra $QJ(3)$ generates potentials that admit exact solution in relativistic and nonrelativistic quantum mechanics. Being a spectrum-generatingdynamic symmetry algebra and possessing the ladder property, $QJ(3)$ makes it possible to find the wave functions in the coordinate representation. The exactly solvable potentials specified in explicit form are regarded as a special case of a larger class of exactly solvable potentials specified implicitly. The connection between classical and quantum problems possessing exact solutions is obtained by means of $QJ(3)$. 
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I. M. Lutsenko. Jacobi algebra and potentials generated by it. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a0/

[1] Sklyanin E. K., Funkts. analiz i ego prilozh., 16:4 (1982), 27–34 ; 17:4 (1983), 34–48 | MR | Zbl | MR | Zbl

[2] Granovskii Ya. I., Zhedanov A. S., Lutsenko I. M., ZhETF, 99:2 (1991), 369–377 | MR

[3] Natanzon G. A., Vestn. LGU. Ser. Fizika, khimiya, 1971, no. 10, 22–28 ; Lemeiux A., Bose A. K., Ann. Inst. Henri Poincare, 10:3 (1969), 259 | MR

[4] Granovskii Ya. I., Zhedanov A. S., Tochno reshaemye zadachi i kvadratichnye algebry, preprint DonFti 89-7, DonFti, Donetsk, 1989

[5] Granovskii Ya. I., Lutzenko I. M., Zhedanov A. S., Ann. Phys., in print | MR

[6] Gal'bert O. F., Granovskii Ya. I., Zhedanov A. S., Phys. Lett. A, 153:4, 5 (1991), 177–180 ; Granovskii Ya. I., Zhedanov A. S., Lutzenko I. M., J. Phys. A, 24 (1991), 3887–3894 ; Грановский Я. И., Жеданов А. С., Луценко И. М., ТМФ, 91:3 (1992), 396–410 | DOI | MR | DOI | MR | MR

[7] Konopelchenko B. G., Rumer Yu. B., DAN SSSR, 220:1 (1975), 58–60 | MR | Zbl

[8] Kuznetsov U. B., J. Math. Phvs., 31:5 (1990), 1167 | DOI | MR | Zbl

[9] Manning M., Fhys. Rev., 48:2 (1935), 161–164 | DOI | Zbl

[10] Landau L. D., Lifshits E. M., Kvantovaya mekhanika, Nauka, M., 1974 | MR

[11] Cyetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1979 ; Бейтмен Г., Эрдейи А., Высшие трансцендентные функции, Наука, М., 1974 | MR | MR

[12] Bagrov V. G., Shapovalov A. V., Shirkov I. V., Izv. vuzov. Fizika, 1989, no. 11, 114–116 | MR

[13] Turbiner A. B., ZhETF, 94:2 (1988), 33–44 ; Заславский О. Б., Ульянов В. В., ЖЭТФ, 87:5 (1984), 1724–1733 | MR | MR