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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Bibliographic Details
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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Summary:	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.