Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems
In this paper we present the solution of the stationary Schrödinger equation in the coordinates and momentumrepresentations for three simple problems: the linear potential, the harmonic oscillator and the Dirac deltapotential. We verify through explicit calculation that the wave functions obtained i...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Pedagógica y Tecnológica de Colombia
- Repositorio:
- RiUPTC: Repositorio Institucional UPTC
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.uptc.edu.co:001/15301
- Acceso en línea:
- https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589
https://repositorio.uptc.edu.co/handle/001/15301
- Palabra clave:
- Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier.
Schrödinger equation, coordinates and momentum representations, Fourier transform.
- Rights
- License
- Derechos de autor 2021 CIENCIA EN DESARROLLO
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2021-01-082024-07-08T14:24:01Z2024-07-08T14:24:01Zhttps://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/1158910.19053/01217488.v12.n1.2021.11589https://repositorio.uptc.edu.co/handle/001/15301In this paper we present the solution of the stationary Schrödinger equation in the coordinates and momentumrepresentations for three simple problems: the linear potential, the harmonic oscillator and the Dirac deltapotential. We verify through explicit calculation that the wave functions obtained in each representationare connected through the Fourier transform, showing that both solutions constitute two complementaryrepresentations of the same quantum state. From a pedagogical point of view, this shows that both solutionscontain information of equal theoretical value and constitute two complementary representations.En este trabajo presentamos la solución de la ecuación de Schrödinger estacionaria en la representaciónde coordenadas y de momento para tres problemas sencillos: el potencial lineal, el oscilador armónicoy el potencial tipo delta de Dirac. Verificamos a través del cálculo explícito que las funciones de ondaobtenidas en cada representación están conectadas a través de la transformada de Fourier, mostrando queambas soluciones constituyen dos representaciones complementarias del mismo estado cuántico. Desde unpunto de vista pedagógico esto muestra que ambas soluciones contienen información de igual valor teóricoy constituyen dos representaciones complementarias.application/pdfspaspaUniversidad Pedagógica y Tecnológica de Colombiahttps://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589/10691Derechos de autor 2021 CIENCIA EN DESARROLLOhttp://purl.org/coar/access_right/c_abf2Ciencia En Desarrollo; Vol. 12 No. 1 (2021): Vol 12, Núm.1 (2021): Enero-Junio; 23-32Ciencia en Desarrollo; Vol. 12 Núm. 1 (2021): Vol 12, Núm.1 (2021): Enero-Junio; 23-322462-76580121-7488Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier.Schrödinger equation, coordinates and momentum representations, Fourier transform.Quantum Mechanics in Coordinate and Moment Representations Through Three Simple ProblemsMecánica Cuántica en las Representaciones de Coordenadas y Momento a Través Tres Problemas Sencillosinfo:eu-repo/semantics/articletextohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Bolaños, E. J.Suescún, D.Rasero Causil, Diego Alejandro001/15301oai:repositorio.uptc.edu.co:001/153012025-07-18 10:56:40.212metadata.onlyhttps://repositorio.uptc.edu.coRepositorio Institucional UPTCrepositorio.uptc@uptc.edu.co |
| dc.title.en-US.fl_str_mv |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems |
| dc.title.es-ES.fl_str_mv |
Mecánica Cuántica en las Representaciones de Coordenadas y Momento a Través Tres Problemas Sencillos |
| title |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems |
| spellingShingle |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. Schrödinger equation, coordinates and momentum representations, Fourier transform. |
| title_short |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems |
| title_full |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems |
| title_fullStr |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems |
| title_full_unstemmed |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems |
| title_sort |
Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems |
| dc.subject.es-ES.fl_str_mv |
Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. |
| topic |
Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. Schrödinger equation, coordinates and momentum representations, Fourier transform. |
| dc.subject.en-US.fl_str_mv |
Schrödinger equation, coordinates and momentum representations, Fourier transform. |
| description |
In this paper we present the solution of the stationary Schrödinger equation in the coordinates and momentumrepresentations for three simple problems: the linear potential, the harmonic oscillator and the Dirac deltapotential. We verify through explicit calculation that the wave functions obtained in each representationare connected through the Fourier transform, showing that both solutions constitute two complementaryrepresentations of the same quantum state. From a pedagogical point of view, this shows that both solutionscontain information of equal theoretical value and constitute two complementary representations. |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2024-07-08T14:24:01Z |
| dc.date.available.none.fl_str_mv |
2024-07-08T14:24:01Z |
| dc.date.none.fl_str_mv |
2021-01-08 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.es-ES.fl_str_mv |
texto |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.none.fl_str_mv |
https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589 10.19053/01217488.v12.n1.2021.11589 |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.uptc.edu.co/handle/001/15301 |
| url |
https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589 https://repositorio.uptc.edu.co/handle/001/15301 |
| identifier_str_mv |
10.19053/01217488.v12.n1.2021.11589 |
| dc.language.none.fl_str_mv |
spa |
| dc.language.iso.none.fl_str_mv |
spa |
| language |
spa |
| dc.relation.none.fl_str_mv |
https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589/10691 |
| dc.rights.es-ES.fl_str_mv |
Derechos de autor 2021 CIENCIA EN DESARROLLO |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| rights_invalid_str_mv |
Derechos de autor 2021 CIENCIA EN DESARROLLO http://purl.org/coar/access_right/c_abf2 |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.es-ES.fl_str_mv |
Universidad Pedagógica y Tecnológica de Colombia |
| dc.source.en-US.fl_str_mv |
Ciencia En Desarrollo; Vol. 12 No. 1 (2021): Vol 12, Núm.1 (2021): Enero-Junio; 23-32 |
| dc.source.es-ES.fl_str_mv |
Ciencia en Desarrollo; Vol. 12 Núm. 1 (2021): Vol 12, Núm.1 (2021): Enero-Junio; 23-32 |
| dc.source.none.fl_str_mv |
2462-7658 0121-7488 |
| institution |
Universidad Pedagógica y Tecnológica de Colombia |
| repository.name.fl_str_mv |
Repositorio Institucional UPTC |
| repository.mail.fl_str_mv |
repositorio.uptc@uptc.edu.co |
| _version_ |
1839633851841773568 |