Artículo
Algebraic DVR Approaches Applied to Describe the Stark Effect
Autor/es | Bermúdez Montaña, Marisol
Rodríguez Arcos, Marisol Lemus, Renato Arias Carrasco, José Miguel Gómez Camacho, Joaquín José Orgaz, Emilio |
Departamento | Universidad de Sevilla. Departamento de Física Atómica, Molecular y Nuclear |
Fecha de publicación | 2020 |
Fecha de depósito | 2020-12-10 |
Publicado en |
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Resumen | Two algebraic approaches based on a discrete variable representation are introduced
and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach
consists of considering an algebraic ... Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators r 2 and p 2 are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the U(4) dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers n = 2, 3 with m = 0. |
Agencias financiadoras | Consejería de Economía, Conocimiento, Empresas y Universidad, Junta de Andalucía Ministerio de Ciencia e Innovación (MICIN). España European Commission (EC) |
Identificador del proyecto | IN-212020
FQM-160 FIS2017-88410-P RTI2018-098117-B-C21 PID2019-104002GB-C22 H2020-INFRAIA-2014-2015 |
Cita | Bermúdez Montaña, M., Rodríguez Arcos, M., Lemus, R., Arias Carrasco, J.M., Gómez Camacho, J.J. y Orgaz, E. (2020). Algebraic DVR Approaches Applied to Describe the Stark Effect. Symmetry, 12 (10), 1-21. |
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