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

• Authors: Nicolae Cotfas
• Languages of publication: 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.

Keywords

EN

Associated special functions; orthogonal polynomials; raising/lowering operators; Schrödinger equation; 02.30.Gp; 03.65.-w

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2004
• Volume: 2
• Issue: 3
• Pages: 456-466

Dates

published

1 - 9 - 2004

online

1 - 9 - 2004

Contributors

author

Nicolae Cotfas

• Faculty of Physics, University of Bucharest, PO Box 76-54, Bucharest, Romania

References

• [1] A.F. Nikiforov, S.K. Suslov, V.B. Uvarov: Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
• [2] N. Cotfas: “Shape invariance, raising and lowering operators, in hypergeometric type equations”, J. Phys. A: Math. Gen., Vol.35, (2002), pp.9355–9365. http://dx.doi.org/10.1088/0305-4470/35/44/306[Crossref]
• [3] F. Cooper, A. Khare, U. Sukhatme: “Supersymmetry and quantum mechanics”, Phys. Rep., Vol.251, (1995), pp.267–385. http://dx.doi.org/10.1016/0370-1573(94)00080-M[Crossref]
• [4] J.W. Dabrowska, A. Khare, U. Sukhatme: “Explicit wavefunctions for shape-invariant potentials by operator techniques”, J. Phys. A: Math. Gen., Vol. 21, (1988), pp. L195-L200. http://dx.doi.org/10.1088/0305-4470/21/4/002[Crossref]
• [5] L. Infeld and T.E. Hull: “The factorization method”, Rev. Mod. Phys., Vol. 23, (1951), pp. 121–68. http://dx.doi.org/10.1103/RevModPhys.23.21[Crossref]
• [6] M.A. Jafarizadeh and H. Fakhri: “Parasupersymmetry and shape invariance in differential equations of mathematical physics and quantum mechanics”, Ann. Phys., NY, Vol. 262, (1998), pp. 260–276. http://dx.doi.org/10.1006/aphy.1997.5745[Crossref]
• [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]

Identifiers

DOI

10.2478/BF02476425