Aplicaciones del cálculo fraccionario en la mecánica cuántica: soluciones numéricas

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dc.audienceComunidad Universidad de Medellínspa
dc.contributor.advisorCorrea Abad, Julián David
dc.contributor.advisorMora Ramos, Miguel Eduardo
dc.contributor.advisorPérez Torres, Jhon Fredy
dc.contributor.authorMedina Torres, Leidy Yoana
dc.coverage.spatialLat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees
dc.coverage.spatialLat: 06 15 00 N  degrees minutes  Lat: 6.2500  decimal degreesLong: 075 36 00 W  degrees minutes  Long: -75.6000  decimal degrees
dc.date2025-01-20
dc.date.accessioned2025-03-10T19:39:12Z
dc.date.available2025-03-10T19:39:12Z
dc.descriptionEn este trabajo se abordaron problemas de mecánica cuántica en una dimensión usando la mecánica cuántica fraccional de Laskin. Se compararon diferentes operadores diferenciales fraccionales específicamente conformable, Riemann-Liouville-Caputo y Riesz para describir el operador de energía cinética. Los estados de energía y las funciones de onda se analizaron para potenciales rectangulares y armónicos, observando diferencias significativas en los valores de energía de los niveles excitados y en las densidades de probabilidad cuando el sistema muestra degeneración. Proporcionaron un enfoque estandarizado para resolver numéricamente la ecuación de Schrodinger fraccional en una dimensión. además, se estudiaron los efectos no adiabáticos en la dinámica nuclear del ion molecular usando la ecuación de Schrodinger fraccional espacial para analizar las vibraciones moleculares, encontrando que la relación de incertidumbre de Heisenberg se mantiene independientemente de la ecuación de Schrodinger fraccional. Finalmente se analizaron las energías y funciones propias de las moléculas H+2 y D+2 , demostrando la aplicabilidad de la ecuación de Schrodinger fraccional para considerar efectos no adiabáticos.spa
dc.descriptionIn this thesis, we investigated unidimensional quantum mechanics problems using Laskin’s fractional quantum mechanics. We compared different fractional differential operators, specifically the conformable, Riemann-Liouville-Caputo, and Riesz operators, to describe the kinetic energy operator. The energy states and wave functions were analyzed for rectangular and harmonic potentials. We observed significant differences in the energy values of the excited levels and the probability densities when the system exhibited degeneration. We provided a standardized approach to solve the unidimensional fractional Schrödinger equation numerically. Furthermore, we studied the nonadiabatic effects in the nuclear dynamics of ion molecules using the fractional spatial Schrödinger equation to analyze molecular vibrations. We found that Heisenberg’s uncertainty relation is preserved independently of the fractional Schrödinger equation. Lastly, we analyzed the eigenenergies and eigenfunctions of the H and D molecules, demonstrating the applicability of the fractional Schrödinger equation in considering nonadiabatic effects.eng
dc.description.degreelevelDoctoradospa
dc.description.degreenameDoctora en Modelación y Ciencia Computacionalspa
dc.format.extentp. 1-88spa
dc.format.mediumElectrónicospa
dc.format.mimetypeapplication/pdf
dc.identifier.instnameinstname:Universidad de Medellínspa
dc.identifier.otherT0606 2024
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.urihttp://hdl.handle.net/11407/8770
dc.language.isospa
dc.publisherUniversidad de Medellínspa
dc.publisherUniversidad de Medellínspa
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.publisher.placeMedellínspa
dc.publisher.programDoctorado en Modelación y Ciencia Computacionalspa
dc.relation.citationendpage88
dc.relation.citationstartpage1
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dc.rights.accessrightsinfo:eurepo/semantics/openAccess
dc.rights.creativecommonsAttribution-NonCommercial-ShareAlike 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0*
dc.subjectMecánica cuántica fraccionariaspa
dc.subjectEcuación de Schrödingerspa
dc.subjectRieszspa
dc.subjectConformable efectos noadiabáticosspa
dc.subjectFractional quantum mechanicseng
dc.subjectConformable formulationeng
dc.subjectFractional Schrödinger Equationeng
dc.subjectNonadiabatic effectseng
dc.subject.lembDiagramas de Feynman
dc.subject.lembDinámica cuántica
dc.subject.lembDinámica molecular
dc.subject.lembEspacios de Riesz
dc.subject.lembFuerza y energía
dc.subject.lembOperador de Schrödinger
dc.subject.lembTeoría cuántica
dc.titleAplicaciones del cálculo fraccionario en la mecánica cuántica: soluciones numéricasspa
dc.typeinfo:eu-repo/semantics/doctoralThesis
dc.type.coarhttp://purl.org/coar/resource_type/c_db06
dc.type.hasversioninfo:eu-repo/semantics/acceptedVersion
dc.type.localTesis Doctoralspa

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