Dynamical Algebras of Hyperbolic Pöschl-Teller Potentials
In this work the Schrödinger equation for hyperbolic Pöschl–Teller (PT) potential is solved algebraically. Two couples of operators are proposed, which allow us to solve the equation by means of the factorization method. The dynamical algebras of the two-parametric hyperbolic Pöschl–Teller Hamiltoni...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Valladolid |
| Repositorio: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:uvadoc.uva.es:10324/43520 |
| Acceso en línea: | http://uvadoc.uva.es/handle/10324/43520 |
| Access Level: | acceso abierto |
| Palabra clave: | Hyperbolic PöschlTeller (PT) potential Actorization method |
| Sumario: | In this work the Schrödinger equation for hyperbolic Pöschl–Teller (PT) potential is solved algebraically. Two couples of operators are proposed, which allow us to solve the equation by means of the factorization method. The dynamical algebras of the two-parametric hyperbolic Pöschl–Teller Hamiltonian hierarchies are obtained. These operators act on the eigenfunctions of each Hamiltonian relating them to the eigenfunctions of a second Hamiltonian. This kind of operators are called “shift” because they change the parameters of the potential but keep the energy. Such operators close the Lie algebra su(1; 1) su(1; 1) which is isomorphic to the so(2; 2) Lie algebra. In the second part of this work, the PT Hamiltonian is obtained starting from the Lie algebra su(1; 1) su(1; 1). First, by building the appropriate representations on a pseudo sphere of three dimensions and afterwards we identify the realizacion of the generators of the algebra with the operators computed by the factorization method. We have also obtained the eigenfunctions by means of both approximations. |
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