1,443 research outputs found
The number radial coherent states for the generalized MICZ-Kepler problem
We study the radial part of the MICZ-Kepler problem in an algebraic way by
using the Lie algebra. We obtain the energy spectrum and the
eigenfunctions of this problem from the theory of unitary
representations and the tilting transformation to the stationary Schr\"odinger
equation. We construct the physical Perelomov number coherent states for this
problem and compute some expectation values. Also, we obtain the time evolution
of these coherent states
Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime
We study a relativistic quantum particle in cosmic string spacetime in the
presence of a uniform magnetic field and a Coulomb-type scalar potential. It is
shown that the radial part of this problem possesses the symmetry. We
obtain the energy spectrum and eigenfunctions of this problem by using two
algebraic methods: the Schr\"odinger factorization and the tilting
transformation. Finally, we give the explicit form of the relativistic coherent
states for this problem.Comment: 21 page
Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
We introduce two generalizations of the Jaynes-Cummings (JC) model for two
modes of oscillation. The first model is formed by two Jaynes-Cummings
interactions, while the second model is written as a simultaneous
Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of
its properties and obtain the energy spectrum and eigenfunctions of these
models by using the tilting transformation and the Perelomov number coherent
states of the two-dimensional harmonic oscillator. Moreover, as physical
applications, we connect these new models with two important and novelty
problems: The relativistic non-degenerate parametric amplifier and the
relativistic problem of two coupled oscillators.Comment: 16 page
Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections
By modifying and generalizing known supersymmetric models we are able to find
four different sets of one-dimensional Hamiltonians for the inverted harmonic
oscillator. The first set of Hamiltonians is derived by extending the
supersymmetric quantum mechanics with reflections to non-Hermitian
supercharges. The second set is obtained by generalizing the supersymmetric
quantum mechanics valid for non-Hermitian supercharges with the Dunkl
derivative instead of . Also, by changing the derivative
by the Dunkl derivative in the creation and annihilation-type
operators of the standard inverted Harmonic oscillator
, we generate the third
set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a
parameter of the supersymmetric two-body Calogero-type model to take imaginary
values. The eigensolutions of definite parity for each set of Hamiltonians are
given
Approach to Stokes Parameters and the Theory of Light Polarization
We introduce an alternative approach to the polarization theory of light.
This is based on a set of quantum operators, constructed from two independent
bosons, being three of them the Lie algebra generators, and the other
one, the Casimir operator of this algebra. By taking the expectation value of
these generators in a two-mode coherent state, their classical limit is
obtained. We use these classical quantities to define the new Stokes-like
parameters. We show that the light polarization ellipse can be written in terms
of the Stokes-like parameters. Also, we write these parameters in terms of
other two quantities, and show that they define a one-sheet (Poincar\'e
hyperboloid) of a two-sheet hyperboloid. Our study is restricted to the case of
a monochromatic plane electromagnetic wave which propagates along the axis
solution for the Dunkl oscillator in two dimensions and its coherent states
We study the Dunkl oscillator in two dimensions by the algebraic
method. We apply the Schr\"odinger factorization to the radial Hamiltonian of
the Dunkl oscillator to find the Lie algebra generators. The energy
spectrum is found by using the theory of unitary irreducible representations.
By solving analytically the Schr\"odinger equation, we construct the Sturmian
basis for the unitary irreducible representations of the Lie algebra.
We construct the Perelomov radial coherent states for this problem
and compute their time evolution.Comment: 14 page
An algebraic approach to a charged particle in an uniform magnetic field
We study the problem of a charged particle in a uniform magnetic field with
two different gauges, known as Landau and symmetric gauges. By using a
similarity transformation in terms of the displacement operator we show that,
for the Landau gauge, the eigenfunctions for this problem are the harmonic
oscillator number coherent states. In the symmetric gauge, we calculate the
Perelomov number coherent states for this problem in cylindrical
coordinates in a closed form. Finally, we show that these Perelomov number
coherent states are related to the harmonic oscillator number coherent states
by the contraction of the group to the Heisenberg-Weyl group.Comment: 11 page
Algebraic solution and coherent states for the Dirac oscillator interacting with the Aharonov-Casher system in the cosmic string background
We introduce an algebraic approach to study the -Dirac
oscillator in the presence of the Aharonov-Casher effect coupled to an external
electromagnetic field in the Minkowski spacetime and the cosmic string
spacetime. This approach is based on a quantum mechanics factorization method
that allows us to obtain the algebra generators, the energy spectrum
and the eigenfunctions. We obtain the coherent states and their temporal
evolution for each spinor component of this problem. Finally, for these
problems, we calculate some matrix elements and the Schr\"odinger uncertainty
relationship for two general operators.Comment: 19 page
Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
We extend the -dimensional Dirac-Moshinsky oscillator by changing the
standard derivative by the Dunkl derivative. We demonstrate in a general way
that for the Dirac-Dunkl oscillator be parity invariant, one of the spinor
component must be even, and the other spinor component must be odd, and vice
versa. We decouple the differential equations for each of the spinor component
and introduce an appropriate algebraic realization for the cases when
one of these functions is even and the other function is odd. The
eigenfunctions and the energy spectrum are obtained by using the
irreducible representation theory. Finally, by setting the Dunkl parameter to
vanish, we show that our results reduce to those of the standard
Dirac-Moshinsky oscillator.Comment: 15 page
Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator
We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing the
standard partial derivatives by the Dunkl derivatives in the standard
Klein--Gordon (KG) equation. We show that the generalization with Dunkl
derivative of the -component of the angular momentum is what allows the
separation of variables of the DKG equation. Then, we compute the energy
spectrum and eigenfunctions of the DKG equations for the 2D Coulomb potential
and the Klein--Gordon oscillator analytically and from an
algebraic point of view. Finally, we show that if the parameters of the Dunkl
derivative vanish, the obtained results suitably reduce to those reported in
the literature for these 2D problems.Comment: 16 page
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