RT info:eu-repo/semantics/masterThesis
T1 Dynamical Algebras of Hyperbolic Pöschl-Teller Potentials
A1 Blázquez Villalobos, María del Carmen
A2 Universidad de Valladolid. Facultad de Ciencias
K1 Hyperbolic PöschlTeller (PT) potential
K1 Actorization method
AB In this work the Schrödinger equation for hyperbolic Pöschl–Teller (PT) potential is solvedalgebraically. Two couples of operators are proposed, which allow us to solve the equation bymeans of the factorization method. The dynamical algebras of the two-parametric hyperbolicPöschl–Teller Hamiltonian hierarchies are obtained. These operators act on the eigenfunctionsof each Hamiltonian relating them to the eigenfunctions of a second Hamiltonian. This kindof operators are called “shift” because they change the parameters of the potential but keepthe energy. Such operators close the Lie algebra su(1; 1)  su(1; 1) which is isomorphic to theso(2; 2) Lie algebra. In the second part of this work, the PT Hamiltonian is obtained startingfrom the Lie algebra su(1; 1) su(1; 1). First, by building the appropriate representations on apseudo sphere of three dimensions and afterwards we identify the realizacion of the generatorsof the algebra with the operators computed by the factorization method. We have also obtainedthe eigenfunctions by means of both approximations.
YR 2020
FD 2020
LK http://uvadoc.uva.es/handle/10324/43520
UL http://uvadoc.uva.es/handle/10324/43520
LA eng
NO Departamento de Física Teórica, Atómica y Óptica
DS UVaDOC
RD 22-nov-2024