Journal ArticleDOI
Duality of two types of SU(1, 1) coherent states and an intermediate type
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TLDR
In this paper, the duality of the operators becomes a self-duality and the corresponding operators form a usual Heisenberg-Weyl algebra, and it is shown that no wavepackets corresponding to any of the SU(1, 1) coherent states can exactly preserve their shape during time evolution.Abstract:
The two types of SU(1, 1) coherent states of Barut and Girardello and of Perelomov are dual in a sense that the operators in the eigenvalue equation and in the exponentials which create these types of coherent states from the lowest eigenstate (vacuum) form an asymmetric Heisenberg–Weyl algebra. A new type of SU(1, 1) coherent states which takes on an intermediate position between the two dual types of SU(1, 1) coherent states already mentioned is established and investigated. In this new type, the duality of the operators becomes a self-duality and the corresponding operators form a usual Heisenberg–Weyl algebra. Properties of the different SU(1, 1) coherent states are investigated for the realization of SU(1, 1) by one-dimensional quantum-mechanical potential problems leading to a quadratic law of energy-level spacing. Coherent SU(1, 1) phase states are discussed for this realization of SU(1, 1). It is shown that no wavepackets corresponding to any of the SU(1, 1) coherent states can exactly preserve their shape during time evolution.read more
Citations
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Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations
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References
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Journal ArticleDOI
Coherent and incoherent states of the radiation field
TL;DR: In this article, the photon statistics of arbitrary fields in fully quantum-mechanical terms are discussed, and a general method of representing the density operator for the field is discussed as well as a simple formulation of a superposition law for photon fields.
Book
Generalized Coherent States and Their Applications
TL;DR: In this paper, the authors define the notion of generalized coherent states and define a generalization of the Coherent State Representation T?(g) of the Heisenberg-Weyl Group.
Book
Practical quantum mechanics
TL;DR: In this paper, one-body problems without spin are discussed. And the Wentzel-Kramers Brillouin (WKB) approximation of the WKB is used.
Journal ArticleDOI
Der stetige Übergang von der Mikro- zur Makromechanik
TL;DR: In this paper, a falshe Verschiebung der Spektrallinie in der Richtung des helleren Teiles des Hintergrundes angibt.
Journal ArticleDOI
Coherent states for arbitrary Lie group
TL;DR: In this paper, the concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie groups and its features are investigated for the simplest Lie groups.