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.
 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/10.1088/0305-4470/35/44/30610.1088/0305-4470/35/44/306Search in Google Scholar
 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. 10.2478/BF02476425Search in Google Scholar
 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-M10.1016/0370-1573(94)00080-MSearch in Google Scholar
 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.1997.574510.1006/aphy.1997.5745Search in Google Scholar
 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/10.1088/0305-4470/21/4/00210.1088/0305-4470/21/4/002Search in Google Scholar
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