The generalized Hulthén potential

Morales, J.; Peña, J. J.; Morales-Guzmán, J. D.

doi:10.1007/s002140000130

Cited by 12 publications

(1 citation statement)

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“…Consequently, according to Equation (3) In a similar way, the selection 0 C = and 0 A B + < permit us to obtain the supersymmetric or generalized Hulthén potential already given by Morales et al, [17]. Also, the selection 0 ,…”

Section: Generalized V(r) From G(x) Proportional To P(x)mentioning

confidence: 71%

Exactly Solvable Schrödinger Equation with Hypergeometric Wavefunctions

Morales¹,

García‐Martínez²,

García-Ravelo³

et al. 2015

JAMP

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In this work, the canonical transformation method is applied to a general second order differential equation (DE) in order to trasform it into a Schrödinger-like DE. Our proposal is based on an auxiliary function g(x) which determines the transformation needed to find exactly-solvable potentials associated to a known DE. To show the usefulness of the proposed approach, we consider explicitly their application to the hypergeometric DE with the aim to find quantum potentials with hypergeometric wavefunctions. As a result, different potentials are obtained depending on the choice of the auxiliary function; the generalized Scarf, Posh-Teller, Eckart and Rosen-Morse trigonometric and hyperbolic potentials, are derived by selecting g(x) as constant and proportional to the P(x) hypergeometric coefficient. Similarly, the choices () () 2 g x P x x and () () 2 g x x P x give rise to a class of exactly-solvable generalized multiparameter exponential-type potentials, which contain as particular cases the Hulthén, Manning-Rosen and Woods-Saxon models, among others. Our proposition is general and can be used with other important DE within the frame of applied matematics and physics.

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Section: Generalized V(r) From G(x) Proportional To P(x)mentioning

confidence: 71%

Exactly Solvable Schrödinger Equation with Hypergeometric Wavefunctions

Morales¹,

García‐Martínez²,

García-Ravelo³

et al. 2015

JAMP

Self Cite

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Solvable quartic potentials and their isospectral partners

Peña

Ovando

Morales‐Guzmán

et al. 2001

Int J of Quantum Chemistry

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ABSTRACT:In this work, we present an operational method based on the use of supersymmetry applied to quantum mechanics, shape invariance, and intertwining techniques to determine certain classes of solvable potentials. Our proposal uses an ansatz which matches the Witten superpotential, allowing us to identify, through a particular Ricatti relationship, the potentials that are solvable as well as to obtain straightforwardly the corresponding ground state eigenvalues, energy, and wave function. As a useful application of the proposed method, we obtain some examples of solvable quartic potentials as well as, with the aid of the standard and generalized Darboux transform, the partner isospectral potentials that are associated with the models under consideration. The method can be easily extended and used to find new solvable potentials which could be useful in the modeling of specific quantum interactions.

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