5 research outputs found
Coherent states \`a la Klauder-Perelomov for the P\"oschl-Teller potentials
In this paper we present a scheme for constructing the coherent states of
Klauder-Perelomov's type for a particle which is trapped in P\"oschl-Teller
potentials
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
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