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2004 | 2 | 3 | 456-466
Article title

Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics

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EN
Abstracts
EN
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The equations considered are directly related to some Schrödinger type equations (Pöschl-Teller, Scarf, Morse, etc), and the special functions defined are related to the corresponding bound-state eigenfunctions.
Publisher
Journal
Year
Volume
2
Issue
3
Pages
456-466
Physical description
Dates
published
1 - 9 - 2004
online
1 - 9 - 2004
References
  • [1] A.F. Nikiforov, S.K. Suslov, V.B. Uvarov: Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
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  • [7] J.-P. Antoine, J.-P. Gazeau, P. Monceau, J.R. Klauder, K.A. Penson: “Temporally stable coherent states for infinite well and Pöschl-Teller potentials”, J. Math. Phys., Vol. 42, (2001), pp. 2349–2387. http://dx.doi.org/10.1063/1.1367328[Crossref]
  • [8] Y. Alhassid, F. Gürsey, F. Iachello: “Group theory approach to scattering”, Ann. Phys. (N.Y.), Vol. 148, (1983), pp. 346–380. http://dx.doi.org/10.1016/0003-4916(83)90244-0[Crossref]
  • [9] P.M. Morse: “Diatomic molecules according to the wave mechanics. II. Vibrational levels”, Phys. Rev., Vol. 34, (1929), pp. 57–64. http://dx.doi.org/10.1103/PhysRev.34.57[Crossref]
  • [10] F.L. Scarf: “New soluble energy band problem”, Phys. Rev., Vol. 112, (1958), pp. 1137–1140. http://dx.doi.org/10.1103/PhysRev.112.1137[Crossref]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_BF02476425
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