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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 2:36 |
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Conference: Bucharest University Faculty of Physics 2007 Meeting
Section: Theoretical Physics and Applied Mathematics Seminar
Title:
Shape invariant hypergeometric type operators and applications
Authors:
Nicolae Cotfas
Affiliation:
Faculty of Physics, University of Bucharest
E-mail
ncotfas@yahoo.com
Keywords:
Hypergeometric type operators, shape invariance, superpotential, raising and lowering operators, Schrodinger equation
Abstract:
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials [1]. The associated special functions are eigenfunctions of some shape invariant operators [2]. These operators can be analyzed together [1,2] and the mathematical formalism we use can be extended in order to define other shape invariant operators [3]. Most of the known exactly solvable Schrodinger equations are directly related to some shape invariant operators, and most of the formulas occurring in the study of these quantum systems follow from a small number of mathematical results concerning the hypergeometric type operators. It is simpler to study these shape invariant operators then the corresponding operators occurring in various applications to quantum mechanics. Our systematic study recovers known results in a natural unified way, and allows one to extend certain results known in particular cases [1,3,4].
References
[1] N. Cotfas: Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics, Central European Journal of Physics 2 (2004) 456-66.
[2] N. Cotfas: Shape invariance, raising and lowering operators in hypergeometric type equations, J. Phys.A: Math. Gen. 35 (2002) 9355-65.
[3] N. Cotfas: Shape invariant hypergeometric type operators with application to quantum mechanics, Central European Journal of Physics 4 (2006) 318-30.
[4] N. Cotfas: http://fpcm5.fizica.unibuc.ro/~ncotfas
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