Topic
Coherent states in mathematical physics
About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.
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TL;DR: The ladder operator formalism of a general quantum state for su(1, 1) Lie algebra is obtained in this paper, where the state bears the generally deformed oscillator algebraic structure.
Abstract: The ladder operator formalism of a general quantum state for su(1, 1) Lie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Perelomov's coherent state is a su(1, 1) nonlinear coherent state. The expansion and the exponential form of the nonlinear coherent state are given. We obtain the matrix elements of the su(1, 1) displacement operator in terms of the hypergeometric functions and the expansions of the displaced number states and Laguerre polynomial states are followed. Finally some interesting su(1, 1) optical systems are discussed.
12 citations
TL;DR: In this article, the normalizable states that minimize the uncertainty product of the oscillator phase operators are determined and some of their physical properties are discussed, and a physical classification of these states has been made and the class of ''analogous'' states to the well-known coherent states is defined.
Abstract: The normalizable states that minimize the uncertainty product of the oscillator phase operators are determined and some of their physical properties are discussed. A physical classification of these states has been made and the class of ``analogous'' states to the well‐known coherent states is physically defined.
12 citations
TL;DR: In this article, the Bloch coherent states for a spin or a system of spins and the Glauber coherent state for bosons are examined from the viewpoint of Lie algebras.
Abstract: The Bloch coherent states for a spin or a system of spins and the Glauber coherent states for bosons are examined from the viewpoint of Lie algebras. It is pointed out that the Bloch coherent states are vectors in the space spanned by the basis functions for an irreducible representation of the unitary unimodular group SU(2), and that the Glauber coherent states are vectors in the space spanned by the basis functions for the infinite‐dimensional irreducible representation of a contracted group of SU(2). A deeper understanding of many of the useful properties of these coherent states is gained.
11 citations
TL;DR: In this paper, a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states is presented, which leads to a useful characterization of extremal POVMs, and it is shown that covariant phase space observables related to squeezed states are extremal while the ones related to number states are not extremal.
Abstract: We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. Positive operator valued measures describe quantum observables and, similarly to quantum states, also quantum observables can be mixed. We show how the formalism of generalized coherent states leads to a useful characterization of extremal POVMs. We prove that covariant phase space observables related to squeezed states are extremal, while the ones related to number states are not extremal.
11 citations
TL;DR: In this paper, the authors studied the properties of all level k coherent states in the context of string theory on a group manifold (WZWN) models and provided the construction of states (i) and compared the two sets and discuss their properties.
11 citations