Shape-invariant hypergeometric type operators with application to quantum mechanics
Languages of publication
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape-invariant operators. These operators can be analysed together and the mathematical formalism we use can be extended in order to define other shape-invariant operators. All the shape-invariant operators considered are directly related to Schrödinger-type equations.
1 - 9 - 2006
1 - 9 - 2006
-  A.F. Nikiforov, S.K. Suslov and V.B. Uvarov: Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
-  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]
-  N. Cotfas: “Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics”, Cent. Eur. J. Phys., Vol. 2, (2004), pp. 456–466. See also http://fpcm5.fizica.unibuc.ro/:_ncotfas.
-  F. Cooper, A. Khare and 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]
-  L. Infeld and T.E. Hull: “The factorization method”, Rev. Mod. Phys., Vol. 23, (1951), pp. 21–68. http://dx.doi.org/10.1103/RevModPhys.23.21[Crossref]
-  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]
-  J.W. Dabrowska, A. Khare and 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]
Publication order reference