155 research outputs found
Generalized coherent and intelligent states for exact solvable quantum systems
The so-called Gazeau-Klauder and Perelomov coherent states are introduced for
an arbitrary quantum system. We give also the general framework to construct
the generalized intelligent states which minimize the Robertson-Schr\"odinger
uncertainty relation. As illustration, the P\"oschl-Teller potentials of
trigonometric type will be chosen. We show the advantage of the analytical
representations of Gazeau-Klauder and Perelomov coherent states in obtaining
the generalized intelligent states in analytical way
Harmonic functions operating in Hermitian Banach
The purpose of this paper is to introduce a harmonic functional calculus in order to generalize some extended versions of theorems of von Neumann, Heinz and Ky Fan
Equicontinuity of power maps in locally pseudo-convex algebras
summary:We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras
Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters
We introduce a special class of truncated Weyl-Heisenberg algebra and discuss
the corresponding Hilbertian and analytical representations. Subsequently, we
study the effect of a quantum network of beam splitting on coherent states of
this nonlinear class of harmonic oscillators. We particularly focus on quantum
networks involving one and two beam splitters and examine the degree of
bipartite as well as tripartite entanglement using the linear entropy
Real analytic version of Lévy’s theorem
We obtain real analytic version of the classical theorem of Lévy on absolutely convergent power series. Whence, as a consequence, its harmonic version.peerReviewe
Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators
This article is an illustration of the construction of coherent and
generalized intelligent states which has been recently proposed by us for an
arbitrary quantum system . We treat the quantum system submitted to the
infinite square well potential and the nonlinear oscillators. By means of the
analytical representation of the coherent states \`{a} la Gazeau-Klauder and
those \`{a} la Klauder-Perelomov, we derive the generalized intelligent states
in analytical ways
The Moyal Bracket in the Coherent States framework
The star product and Moyal bracket are introduced using the coherent states
corresponding to quantum systems with non-linear spectra. Two kinds of coherent
state are considered. The first kind is the set of Gazeau-Klauder coherent
states and the second kind are constructed following the Perelomov-Klauder
approach. The particular case of the harmonic oscillator is also discussed.Comment: 13 page
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