53 research outputs found
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
Graded q-pseudo-differential Operators and Supersymmetric Algebras
We give a supersymmetric generalization of the sine algebra and the quantum
algebra . Making use of the -pseudo-differential operators
graded with a fermionic algebra, we obtain a supersymmetric extension of sine
algebra. With this scheme we also get a quantum superalgebra .Comment: 10 pages, Late
Quantum statistical properties of some new classes of intelligent states associated with special quantum systems
Based on the {\it nonlinear coherent states} method, a general and simple
algebraic formalism for the construction of \textit{`-deformed intelligent
states'} has been introduced. The structure has the potentiality to apply to
systems with a known discrete spectrum as well as the generalized coherent
states with known nonlinearity function . As some physical appearance of
the proposed formalism, a few new classes of intelligent states associated with
\textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'}
and \textit{`hydrogen-like spectrum'} have been realized. Finally, the
nonclassicality of the obtained states has been investigated. To achieve this
purpose the quantum statistical properties using the Mandel parameter and the
squeezing of the quadratures of the radiation field corresponding to the
introduced states have been established numerically.Comment: 13page
Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
We show that the integer quantum Hall effect systems in plane, sphere or
disc, can be formulated in terms of an algebraic unified scheme. This can be
achieved by making use of a generalized Weyl--Heisenberg algebra and
investigating its basic features. We study the electromagnetic excitation and
derive the Hamiltonian for droplets of fermions on a two-dimensional Bargmann
space (phase space). This excitation is introduced through a deformation
(perturbation) of the symplectic structure of the phase space. We show the
major role of Moser's lemma in dressing procedure, which allows us to eliminate
the fluctuations of the symplectic structure. We discuss the emergence of the
Seiberg--Witten map and generation of an abelian noncommutative gauge field in
the theory. As illustration of our model, we give the action describing the
electromagnetic excitation of a quantum Hall droplet in two-dimensional
manifold.Comment: 23 page
Shape invariant potential formalism for photon-added coherent state construction
An algebro-operator approach, called shape invariant potential method, of
constructing generalized coherent states for photon-added particle system is
presented. Illustration is given on Poschl-Teller potential
Generalized Intelligent States for an Arbitrary Quantum System
Generalized Intelligent States (coherent and squeezed states) are derived for
an arbitrary quantum system by using the minimization of the so-called
Robertson-Schr\"odinger uncertainty relation. The Fock-Bargmann representation
is also considered. As a direct illustration of our construction, the
P\"oschl-Teller potentials of trigonometric type will be shosen. We will show
the advantage of the Fock-Bargmann representation in obtaining the generalized
intelligent states in an analytical way. Many properties of these states are
studied
Coherent states for exactly solvable potentials
A general algebraic procedure for constructing coherent states of a wide
class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is
given. The method, {\it a priori}, is potential independent and connects with
earlier developed ones, including the oscillator based approaches for coherent
states and their generalizations. This approach can be straightforwardly
extended to construct more general coherent states for the quantum mechanical
potential problems, like the nonlinear coherent states for the oscillators. The
time evolution properties of some of these coherent states, show revival and
fractional revival, as manifested in the autocorrelation functions, as well as,
in the quantum carpet structures.Comment: 11 pages, 4 eps figures, uses graphicx packag
An approach to construct wave packets with complete classical-quantum correspondence in non-relativistic quantum mechanics
We introduce a method to construct wave packets with complete classical and
quantum correspondence in one-dimensional non-relativistic quantum mechanics.
First, we consider two similar oscillators with equal total energy. In
classical domain, we can easily solve this model and obtain the trajectories in
the space of variables. This picture in the quantum level is equivalent with a
hyperbolic partial differential equation which gives us a freedom for choosing
the initial wave function and its initial slope. By taking advantage of this
freedom, we propose a method to choose an appropriate initial condition which
is independent from the form of the oscillators. We then construct the wave
packets for some cases and show that these wave packets closely follow the
whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm
interpretation of quantum mechanics to quantify this correspondence and show
that the resulting Bohmian trajectories are also in a complete agreement with
their classical counterparts.Comment: 15 pages, 13 figures, to appear in International Journal of
Theoretical Physic
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