RT info:eu-repo/semantics/doctoralThesis
T1 Transformadas supersimétricas de sistemas cuánticos unidimensionales
A1 San Millán Carpintero, Carlos
A2 Universidad de Valladolid. Escuela de Doctorado
K1 Quanta, Teoría de los
K1 Supersymmetry
K1 Supersimetría
K1 One dimmensional systems
K1 Sistemas unidimensionales
K1 Quantum Mechanics
K1 Mecánica Cuántica
K1 2212 Física Teórica
AB This thesis presents a study of various supersymmetric transformations applied to certain one-dimensional quantum mechanics problems. Two systems have been addressed: the free Hamiltonian restricted to an interval of the real line, and the hyperbolic Rosen-Morse potential.The first part of this work involved studying the self-adjoint extensions of the one-dimensional free Hamiltonian restricted to a symmetric interval $(−a,a)$. This involved characterizing the spectrum and wave functions associated with each of the self-adjoint extensions. Subsequent transformations of the obtained extensions led to new one-dimensional quantum systems, which could not have been derived from the typical solutions found in textbooks.The second part focuses on the study of the poles of the S-matrix associated with the Rosen-Morse II potential. The study of this non-symmetric potential results in the emergence of a type of pole that has been little studied in recent literature. The asymptotic analysis results of this potential were used to derive different types of supersymmetry.Furthermore, new relationships for the exchange operators of this potential have been derived. These may, in the future, enable the derivation of simplified versions of the ladder operators associated with this system.
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/67883
UL https://uvadoc.uva.es/handle/10324/67883
LA spa
NO Escuela de Doctorado
DS UVaDOC
RD 22-dic-2024