dorsal/arxiv
View SchemaBargmann representations for deformed harmonic oscillators
| Authors | M. Irac-Astaud, G. Rideau |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9707020 |
| URL | https://arxiv.org/abs/q-alg/9707020 |
| DOI | 10.1142/S0129055X98000343 |
Abstract
Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by four operators $a, a^\dagger, N$ and the unity 1 such as $[a,N] = a, [a^\dagger,N] = -a^\dagger$, $a^\dagger a = \psi(N)$ and $aa^\dagger =\psi(N+1)$. We discuss the conditions of existence of a scalar product expressed with a true integral on the space spanned by the eigenstates of $a$ (or $a^\dagger$). We give various examples, in particular we consider functions $\psi$ that are linear combinations of $q^N$, $q^{-N}$ and unity and that correspond to q-oscillators with Fock-representations or with non-Fock-representations.
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"abstract": "Generalizing the case of the usual harmonic oscillator, we look for Bargmann\nrepresentations corresponding to deformed harmonic oscillators. Deformed\nharmonic oscillator algebras are generated by four operators $a, a^\\dagger, N$\nand the unity 1 such as $[a,N] = a, [a^\\dagger,N] = -a^\\dagger$, $a^\\dagger a =\n\\psi(N)$ and $aa^\\dagger =\\psi(N+1)$. We discuss the conditions of existence of\na scalar product expressed with a true integral on the space spanned by the\neigenstates of $a$ (or $a^\\dagger$). We give various examples, in particular we\nconsider functions $\\psi$ that are linear combinations of $q^N$, $q^{-N}$ and\nunity and that correspond to q-oscillators with Fock-representations or with\nnon-Fock-representations.",
"arxiv_id": "q-alg/9707020",
"authors": [
"M. Irac-Astaud",
"G. Rideau"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1142/S0129055X98000343",
"title": "Bargmann representations for deformed harmonic oscillators",
"url": "https://arxiv.org/abs/q-alg/9707020"
},
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