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: In this article, the growth of analytic functions is intimately connected to the completeness of the sequences of these generalized coherent states, and the least density that such sequences must have in order to be overcomplete is calculated.
Abstract: Analytic representations based on generalized coherent states are studied. The growth of the analytic functions is intimately connected to the completeness of the sequences of these generalized coherent states. The least density that such sequences must have in order to be overcomplete is calculated. The results generalize known results on the completeness of von Neumann lattices for the standard coherent states to other sets of coherent states.
5 citations
01 Jan 1982
TL;DR: In this paper, the authors focus on a method which is the analytic complement to the group theory point of view, and discuss the properties and time evolution of these states, always keeping in mind the desire to find quantum states which follow the classical motion.
Abstract: From the motivation of Schroedinger, that of finding states which follow the motion which a classical particle would have in a given potential, we discuss generalizations of the coherent states of the harmonic oscillator. We focus on a method which is the analytic complement to the group theory point of view. It uses a minimum uncertainty formalism as its basis. We discuss the properties and time evolution of these states, always keeping in mind the desire to find quantum states which follow the classical motion.
5 citations
TL;DR: When the potential is the Fourier transform of a totally finite complex-valued measure, a formula for the one-parameter unitary group generated by the Schrodinger operator in L2 (IRn) is obtained entirely in terms of the basic field operators in a suitable Fock space by means of quantum stochastic calculus.
Abstract: When the potential is the Fourier transform of a totally finite complex-valued measure, a formula for the one-parameter unitary group generated by the Schrodinger operator in L2 (IRn) is obtained entirely in terms of the basic field operators in a suitable Fock space by means of quantum stochastic calculus.
5 citations
TL;DR: In this paper, a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space is presented, which is both simpler and more general than the known ones.
Abstract: We present a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space. Among the new features, in the first place, there is a new formulation of adaptedness which is both simpler and more general than the known ones. The new adaptedness allows for processes which are not restricted to be elements of some norm closure of the ∗-algebra which is generated by the basic creation processes.
5 citations
TL;DR: In this paper, the evolution of a time-dependent quantum system can be described by the dynamics of its generalized coherent state and its phase properties can be investigated by an Hermitian phase operator constructed from a generalized phase state.
5 citations