Hilbert spaces of analytic functions and generalized coherent states
- 1 April 1976
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 17 (4) , 524-527
- https://doi.org/10.1063/1.522937
Abstract
Generalized coherent states which are associated with a generalization of the harmonic oscillator commutation relation are investigated. It is shown that these states form an overcomplete basis in a Hilbert space of analytic functions. The generalized creation and annihilation operators are bounded except in a limit in which they reduce to the usual boson creation and annihilation operators. In this limit the Hilbert space of analytic functions reduces to the Bargmann–Segal Hilbert space of entire functions and in another limit it reduces to the Hardy–Lebesgue space.Keywords
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