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Exactly Solvable Schrodinger Equation with Hypergeometric Wavefunctions
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作者 J.Morales J.García-Martínez +1 位作者 J.García-Ravelo J.J.Pena 《Journal of Applied Mathematics and Physics》 2015年第11期1454-1471,共18页
In this work, the canonical transformation method is applied to a general second order differential equation (DE) in order to trasform it into a Schr?dinger-like DE. Our proposal is based on an auxiliary function g(x)... In this work, the canonical transformation method is applied to a general second order differential equation (DE) in order to trasform it into a Schr?dinger-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 g(x)~P(x)/x2 and g(x)~x2/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. 展开更多
关键词 Canonical Transformation Schrodinger-Like Equation Hypergeometric DE exactly-solvable Potentials
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