2,489 research outputs found
SU(2) Symmetry and Degeneracy From SUSY QM of a Neutron in the Magnetic Field of a Linear Current
From SUSY ladder operators in momentum space of a neutron in the magnetic
field of a linear current, we construct matrix operators that
together with the z-component of the angular momentum satisfy the su(2) Lie
algebra. We use this fact to explain the degeneracy of the energy spectrum
The SU(1,1) Perelomov number coherent states and the non-degenerate parametric amplifier
We construct the Perelomov number coherent states for any three Lie
algebra generators and study some of their properties. We introduce three
operators which act on Perelomov number coherent states and close the
Lie algebra. We show that the most general coherence-preserving
Hamiltonian has the Perelomov number coherent states as eigenfunctions, and we
obtain their time evolution. We apply our results to obtain the non-degenerate
parametric amplifier eigenfunctions, which are shown to be the Perelomov number
coherent states of the two-dimensional harmonic oscillator
coherent states for Dirac-Kepler-Coulomb problem in dimensions with scalar and vector potentials
We decouple the Dirac's radial equations in dimensions with
Coulomb-type scalar and vector potentials through appropriate transformations.
We study each of these uncoupled second-order equations in an algebraic way by
using an algebra realization. Based on the theory of irreducible
representations, we find the energy spectrum and the radial eigenfunctions. We
construct the Perelomov coherent states for the Sturmian basis, which is the
basis for the unitary irreducible representation of the Lie algebra.
The physical radial coherent states for our problem are obtained by applying
the inverse original transformations to the Sturmian coherent states
A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
We introduce a generalization of the Jaynes-Cummings model and study some of
its properties. We obtain the energy spectrum and eigenfunctions of this model
by using the tilting transformation and the squeezed number states of the
one-dimensional har- monic oscillator. As physical applications, we connect
this new model to two important and novelty problems: the relativistic
parametric amplifier and the quantum simulation of a single trapped ion.Comment: This paper was published onder the title "A generalized
Jaynes-Cummings model: The relativistic parametric amplifier and a single
trapped ion
The su(1,1) Dynamical Algebra for the Generalized MICZ-Kepler Problem from the Schr\"odinger Factorization
We apply the Schr\"odinger factorization to construct the generators of the
dynamical algebra for the radial equation of the generalized
MICZ-Kepler problem.Comment: 11 page
On the supersymmetry of the Dirac-Kepler problem plus a Coulomb-type scalar potential in D+1 dimensions and the generalized Lippmann-Johnson operator
We study the Dirac-Kepler problem plus a Coulomb-type scalar potential by
generalizing the Lippmann-Johnson operator to D spatial dimensions. From this
operator, we construct the supersymmetric generators to obtain the energy
spectrum for discrete excited eigenstates and the radial spinor for the SUSY
ground stat
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
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
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
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
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