Geodesic
On the wave functions of a covariant linear oscillator
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 241-247 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the wave functions of a covariant linear oscillator can be expressed via $q$-Hermite polynomials. The corresponding Fourier transforms areobtained. 
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N. M. Atakishiyev; Sh. M. Nagiyev. On the wave functions of a covariant linear oscillator. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 241-247. http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a5/

[1] Kagramanov E. D., Mir-Kasimov R. M., Nagiyev Sh. M., J. Math. Phys., 31:7 (1990), 1733–1738 | DOI | MR | Zbl

[2] Askey R. A., Ismail M. E. H., “A generalization of ultraspherical polynomials”, Studies in Pure Mathematics, Birkhäuser, Basel, 1983, 55–78 | DOI | MR

[3] Atakishiyev N. M., Frank A., Wolf K. B., “A simple difference realization of the Heisenberg $q$-algebra”, J. Math. Phys., 35:7 (1994), 3253–3260 | DOI | MR | Zbl

[4] Askey R. A., “Continuous $q$-Hermite polynomials when $q>1$”, $q$-series and partitions (Minneapolis, MN, 1988), IMA Vol. Math. Appl., 18, Springer, New York, 1989, 151–158 | DOI | MR

[5] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, t. 2, Fizmatgiz, M., 1963

[6] Gasper G., Rahman M., Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990 ; Gasper Dzh., Rakhman M., Bazisnye gipergeometricheskie ryady, Mir, M., 1993 | MR | Zbl | MR | Zbl

[7] Viner N., Integral Fure i nekotorye ego prilozheniya, Fizmatgiz, M., 1963

[8] Mir-Kasimov R. M., J. Phys. A: Math. Gen., 24:18 (1991), 4283–4308 | DOI | MR

[9] Atakishiyev N. M., Suslov S. K., Revista Mexicana de Fisica, 34:2 (1988), 152–167 | MR | Zbl