dorsal/arxiv
View SchemaSimple quantum systems in the momentum representation
| Authors | H. N. Núñez-Yépez, E. Guillaumín-España, R. P. Martínez-y-Romero, A. L. Salas-Brito |
|---|---|
| Categories | |
| ArXiv ID | physics/0001030 |
| URL | https://arxiv.org/abs/physics/0001030 |
Abstract
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In this work, we give an introduction to quantum mechanics in momentum space, where the Schr\"odinger equation becomes an integral equation. To this end we discuss standard problems, namely, the free particle, the quantum motion under a constant potential, a particle interacting with a potential step, and the motion of a particle under a harmonic potential. What is not so standard is that they are all conceived from momentum space and hence they, with the exception of the free particle, are not equivalent to the coordinate space ones with the same names. All the problems are solved within the momentum representation making no reference to the systems they correspond to in the coordinate representation.
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"abstract": "The momentum representation is seldom used in quantum mechanics courses. Some\nstudents are thence surprised by the change in viewpoint when, in doing\nadvanced work, they have to use the momentum rather than the coordinate\nrepresentation. In this work, we give an introduction to quantum mechanics in\nmomentum space, where the Schr\\\"odinger equation becomes an integral equation.\nTo this end we discuss standard problems, namely, the free particle, the\nquantum motion under a constant potential, a particle interacting with a\npotential step, and the motion of a particle under a harmonic potential. What\nis not so standard is that they are all conceived from momentum space and hence\nthey, with the exception of the free particle, are not equivalent to the\ncoordinate space ones with the same names. All the problems are solved within\nthe momentum representation making no reference to the systems they correspond\nto in the coordinate representation.",
"arxiv_id": "physics/0001030",
"authors": [
"H. N. N\u00fa\u00f1ez-Y\u00e9pez",
"E. Guillaum\u00edn-Espa\u00f1a",
"R. P. Mart\u00ednez-y-Romero",
"A. L. Salas-Brito"
],
"categories": [
"physics.ed-ph",
"physics.gen-ph"
],
"title": "Simple quantum systems in the momentum representation",
"url": "https://arxiv.org/abs/physics/0001030"
},
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