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  1. 3 Open Physics

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  1. 1 2009

  2. 1 2006

  3. 1 2004

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  1. 3 Cotfas N.

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

100%
Cotfas N.
Open Physics
|
2004
|
vol. 2
|
issue 3
456-466
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.
2
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Gazeau-Klauder type coherent states for hypergeometric type operators

100%
Cotfas N.
Open Physics
|
2009
|
vol. 7
|
issue 1
147-159
EN
Hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitely described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the parameters involved. We study the parameter dependence of orthogonality, square integrability and monotony of the eigenvalue sequence. The results obtained allow us to define certain systems of Gazeau-Klauder type coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural, unified way and also leads to new findings.
3
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Shape-invariant hypergeometric type operators with application to quantum mechanics

100%
Cotfas N.
Open Physics
|
2006
|
vol. 4
|
issue 3
318-330
EN
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.
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