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...

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Main Authors:	Bolaños, E. J., Suescún, D., Rasero Causil, Diego Alejandro
Format:	Online
Language:	spa
Published:	Universidad Pedagógica y Tecnológica de Colombia 2021
Subjects:	Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. Schrödinger equation, coordinates and momentum representations, Fourier transform.
Online Access:	https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589

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author	Bolaños, E. J. Suescún, D. Rasero Causil, Diego Alejandro
author_facet	Bolaños, E. J. Suescún, D. Rasero Causil, Diego Alejandro
author_sort	Bolaños, E. J.
collection	OJS
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.
format	Online
id	oai:oai.revistas.uptc.edu.co:article-11589
institution	Revista Ciencia en Desarrollo
language	spa
publishDate	2021
publisher	Universidad Pedagógica y Tecnológica de Colombia
record_format	ojs
spelling	oai:oai.revistas.uptc.edu.co:article-115892021-12-14T02:35:17Z Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems Mecánica Cuántica en las Representaciones de Coordenadas y Momento a Través Tres Problemas Sencillos Bolaños, E. J. Suescún, D. Rasero Causil, Diego Alejandro Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. Schrödinger equation, coordinates and momentum representations, Fourier transform. 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. 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. Universidad Pedagógica y Tecnológica de Colombia 2021-01-08 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion texto application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589 10.19053/01217488.v12.n1.2021.11589 Ciencia En Desarrollo; Vol. 12 No. 1 (2021): Vol 12, Núm.1 (2021): Enero-Junio; 23-32 Ciencia en Desarrollo; Vol. 12 Núm. 1 (2021): Vol 12, Núm.1 (2021): Enero-Junio; 23-32 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589/10691 Derechos de autor 2021 CIENCIA EN DESARROLLO
spellingShingle	Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. Schrödinger equation, coordinates and momentum representations, Fourier transform. Bolaños, E. J. Suescún, D. Rasero Causil, Diego Alejandro Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems
title	Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems
title_alt	Mecánica Cuántica en las Representaciones de Coordenadas y Momento a Través Tres Problemas Sencillos
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_short	Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems
title_sort	quantum mechanics in coordinate and moment representations through three simple problems
topic	Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. Schrödinger equation, coordinates and momentum representations, Fourier transform.
topic_facet	Ecuación de Schrödinger, representación de coordenadas y de momento, transformada de Fourier. Schrödinger equation, coordinates and momentum representations, Fourier transform.
url	https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/11589
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