2026-05-05T19:59:17Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/583192023-01-17T20:01:46Zcom_10324_38col_10324_852

Olmo Martínez, Mariano Antonio del Negro Vadillo, Francisco Javier Reyes Guerrero, Jorge Universidad de Valladolid. Facultad de Ciencias 2023-01-17T16:40:18Z 2023-01-17T16:40:18Z 2021 https://uvadoc.uva.es/handle/10324/58319 Este trabajo estudia los sistemas integrables y superintegrables en bajas dimensiones proponiendo un método para su obtención. Se particulariza dicho análisis a la MASA nilpotente de su(1,1), la cual nos lleva al bien conocido potencial Morse. Formulado este, se plantean las factorizaciones tanto clásica como cuántica del Hamiltoniano asociado a dicho potencial. The aim of the study we are about to conduct is to go in depth in the properties of integrable low dimensional systems by the construcction, factorization, and resolution of the Morse 1-dimensional one. In this way, we will begin with a review of the basics that justify and define this analysis. Here, we will discuss about the Algebra, the Lie groups, and other mathematical notions closely linked with the symmetries that characterize this systems.We will remember also, the standart elements typical of the hamiltonian mechanic, from the classic point of view as well as the quantum one, which we will work with in our following factorization. Then, we will delve into this integrable systems, showing his properties, relating them with the superintegrable ones and suggesting a general method to build them. After this introductory parragraph, we will fix this notions to our Morse potential offer. In the next sections, we will use the Hamiltonian built to split it with a classical and quantum factorization, considering the interchange operators, the obtaining and ploting of eigenstates, and the determination of the symmetry relations and their group behavior. Finally, we will conclude our study with a few considetations about the whole proces, the techniques applied, etc. Departamento de Física Teórica, Atómica y Óptica Grado en Física application/pdf spa info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional Sistemas integrables Superintegrables Morse Sistemas integrables y superintegrables en bajas dimensiones: el potencial Morse info:eu-repo/semantics/bachelorThesis