A master function approach for describing shape invariance parameters

Fakhri, H.; Yagoobi, S. K. A. Seyed

doi:10.1088/0305-4470/34/46/309

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…Lorente has shown recently [15,16] that a factorization of H 0 can be obtained by using the three term recurrence relation (7) and a consequence of Rodrigues formula. Following Lorente's idea we obtain a factorization of H m by using (10) and a three term recurrence relation.…”

Section: Raising and Lowering Operators Shape Invariancementioning

confidence: 99%

Shape invariance, raising and lowering operators in hypergeometric type equations

Cotfas

2002

J. Phys. A: Math. Gen.

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The Schrödinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in a supersymmetric approach to these Hamiltonians are consequences of some formulae concerning the general theory of associated special functions. We use this connection in order to obtain a general theory of Schrödinger equations exactly solvable in terms of associated special functions, and to extend certain results known in the case of some particular potentials.

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Section: Raising and Lowering Operators Shape Invariancementioning

confidence: 99%

Shape invariance, raising and lowering operators in hypergeometric type equations

Cotfas

2002

J. Phys. A: Math. Gen.

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Raising and Lowering of Generalized Hulthén Potential from Supersymmetry Approaches

Sadeghi

2007

Int J Theor Phys

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We obtain the exact bound states of the generalized of Hulthén potential with negative energy levels using an analytic approach. In order to obtain bound states, we use the associated Jacobi differential equation. Using the supersymmetry approach to quantum mechanics, we show that these bound states, via four pairs of first order differential operators, represent four types of ladder equations. Two types of these supersymmetric structures suggest derivation of algebric solutions for the bound states using two different approaches. Supersymmetry in quantum mechanics is based on the concept of factorization in the context of shape invariant quantum mechanical problems. If a quantum mechanical problem possesses supersymmetry, we can then factorize the Hamiltonian of the system in terms of a product of first order differential operators leading to shape invariant equations. In this approach, the Hamiltonian is decomposed once in terms of the product of raising and lowering operators and once again as the product of lowering and raising operators, in such a way that the corresponding quantum states of successive levels, are their eigen-states . These Hamiltonians are called supersymmetric partner of each other. In fact, the three separate topics, the factorization method, supersymmetry in quantum mechanics and shape invariance, nowadays have converged to each other. Initially the factorization method was suggested by Darboux (1996) and Schrödinger (1940, 1941a applied it to quantum mechanics. Infeld and Hull (1951) in their review article have studied a large variety of second order differential equations

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Continuous Spectrum of Trigonometric Rosen-Morse and Eckart Potentials from Free Particle Spectrum

Panahi¹,

Pouraram²

2011

Commun. Theor. Phys.

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A master function approach for describing shape invariance parameters

Cited by 5 publications

References 23 publications

Shape invariance, raising and lowering operators in hypergeometric type equations

Shape invariance, raising and lowering operators in hypergeometric type equations

Raising and Lowering of Generalized Hulthén Potential from Supersymmetry Approaches

Continuous Spectrum of Trigonometric Rosen-Morse and Eckart Potentials from Free Particle Spectrum

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