dorsal/arxiv
View SchemaQuantum Mechanics on discrete space and time
| Authors | M. Lorente |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401004 |
| URL | https://arxiv.org/abs/quant-ph/0401004 |
Abstract
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
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"abstract": "We propose the assumption of quantum mechanics on a discrete space and time,\nwhich implies the modification of mathematical expressions for some postulates\nof quantum mechanics. In particular we have a Hilbert space where the vectors\nare complex functions of discrete variable. As a concrete example we develop a\ndiscrete analog of the one-dimensional quantum harmonic oscillator, using the\ndependence of the Wigner functions in terms of Kravchuk polynomials. In this\nmodel the position operator has a discrete spectrum given by one index of the\nWigner functions, in the same way that the energy eigenvalues are given by the\nother matricial index. Similar picture can be made for other models where the\ndifferential equation and their solutions correspond to the continuous limit of\nsome difference operator and orthogonal polynomial of discrete variable.",
"arxiv_id": "quant-ph/0401004",
"authors": [
"M. Lorente"
],
"categories": [
"quant-ph"
],
"title": "Quantum Mechanics on discrete space and time",
"url": "https://arxiv.org/abs/quant-ph/0401004"
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