2,084 research outputs found
Any l-state analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential
The radial part of the Klein-Gordon equation for the Woods-Saxon potential is
solved. In our calculations, we have applied the Nikiforov-Uvarov method by
using the Pekeris approximation to the centrifugal potential for any
states. The exact bound state energy eigenvalues and the corresponding
eigenfunctions are obtained on the various values of the quantum numbers
and . The non-relativistic limit of the bound state energy spectrum was also
found.Comment: 15 pages, 1 tabl
Analytical solutions of the Schr\"{o}dinger equation with the Woods-Saxon potential for arbitrary state
In this work, the analytical solution of the radial Schr\"{o}dinger equation
for the Woods-Saxon potential is presented. In our calculations, we have
applied the Nikiforov-Uvarov method by using the Pekeris approximation to the
centrifugal potential for arbitrary states. The bound state energy
eigenvalues and corresponding eigenfunctions are obtained for various values of
and quantum numbers.Comment: 14 page
Magnetic field driven instability of charged center in graphene
It is shown that a magnetic field dramatically affects the problem of
supercritical charge in graphene making any charge in gapless theory
supercritical. The cases of radially symmetric potential well and Coulomb
center in an homogeneous magnetic field are considered. The local density of
states and polarization charge density are calculated in the first order of
perturbation theory. It is argued that the magnetically induced instability of
the supercritical Coulomb center can be considered as a quantum mechanical
counterpart of the magnetic catalysis phenomenon in graphene.Comment: 10 pages, 4 figures; to be published in PR
Pair creation by a photon in a strong magnetic field
The process of pair creation by a photon in a strong magnetic field is
investigated basing on the polarization operator in the field. The total
probability of the process is found in a relatively simple form. The
probability exhibits a "saw-tooth" pattern because of divergences arising when
the electron and positron are created at threshold of the Landau energy levels.
The pattern will be washed out at averaging over any smooth photon energy
distribution. The new results are obtained in the scope of the quasiclassical
approach: 1) in the case when the magnetic field is the
critical field) the new formulation extends the photon energy interval to the
case when the created particles are not ultrarelativistic; 2) the correction to
the standard quasiclassical approximation is found showing the range of
applicability of the approach at high photon energy as well. The very important
conclusion is that for both cases and the results of
the quasiclassical calculation are very close to averaged probabilities of
exact theory in a very wide range of photon energies. The quasiclassical
approximation is valid also for the energy distribution if the electron and
positron are created on enough high levels.Comment: 21 pages, 6 figure
Universal low-energy properties of three two-dimensional particles
Universal low-energy properties are studied for three identical bosons
confined in two dimensions. The short-range pair-wise interaction in the
low-energy limit is described by means of the boundary condition model. The
wave function is expanded in a set of eigenfunctions on the hypersphere and the
system of hyper-radial equations is used to obtain analytical and numerical
results. Within the framework of this method, exact analytical expressions are
derived for the eigenpotentials and the coupling terms of hyper-radial
equations. The derivation of the coupling terms is generally applicable to a
variety of three-body problems provided the interaction is described by the
boundary condition model. The asymptotic form of the total wave function at a
small and a large hyper-radius is studied and the universal logarithmic
dependence in the vicinity of the triple-collision point is
derived. Precise three-body binding energies and the scattering length
are calculated.Comment: 30 pages with 13 figure
Optical Tomography of Photon-Added Coherent States, Even/Odd Coherent States and Thermal States
Explicit expressions for optical tomograms of the photon-added coherent
states, even/odd photon-added coherent states and photon-added thermal states
are given in terms of Hermite polynomials. Suggestions for experimental
homodyne detection of the considered photon states are presented.Comment: 10 pages, 8 figure
Electromagnetic vortex lines riding atop null solutions of the Maxwell equations
New method of introducing vortex lines of the electromagnetic field is
outlined. The vortex lines arise when a complex Riemann-Silberstein vector
is multiplied by a complex scalar function
. Such a multiplication may lead to new solutions of the Maxwell
equations only when the electromagnetic field is null, i.e. when both
relativistic invariants vanish. In general, zeroes of the function give
rise to electromagnetic vortices. The description of these vortices benefits
from the ideas of Penrose, Robinson and Trautman developed in general
relativity.Comment: NATO Workshop on Singular Optics 2003 To appear in Journal of Optics
NJL interaction derived from QCD: vector and axial-vector mesons
In previous works effective non-local NJL model was
derived in the framework of the fundamental QCD. All the parameters of the
model are expressed through QCD parameters: current light quark mass and
average non-perturbative . The results for scalar and pseudo-scalar
mesons are in satisfactory agreement to existing data. In the present work the
same model without introduction of any additional parameters is applied for a
description of masses and strong decay widths of - and -mesons. The
results for both scalar and vector sectors agree with data with only one
adjusted parameter , with account of average ,
which is obtained in a previous work as well.Comment: 19 pages, 2 figures, 1 tabl
Gauged Nambu-Jona-Lasinio model with extra dimensions
We investigate phase structure of the D (> 4)-dimensional gauged
Nambu-Jona-Lasinio (NJL) model with extra dimensions
compactified on TeV scale, based on the improved ladder Schwinger-Dyson (SD)
equation in the bulk. We assume that the bulk running gauge coupling in the SD
equation for the SU(N_c) gauge theory with N_f massless flavors is given by the
truncated Kaluza-Klein effective theory and hence has a nontrivial ultraviolet
fixed point (UVFP). We find the critical line in the parameter space of two
couplings, the gauge coupling and the four-fermion coupling, which is similar
to that of the gauged NJL model with fixed (walking) gauge coupling in four
dimensions. It is shown that in the presence of such walking gauge interactions
the four-fermion interactions become ``nontrivial'' even in higher dimensions,
similarly to the four-dimensional gauged NJL model. Such a nontriviality holds
only in the restricted region of the critical line (``nontrivial window'') with
the gauge coupling larger than a non-vanishing value (``marginal triviality
(MT)'' point), in contrast to the four-dimensional case where such a
nontriviality holds for all regions of the critical line except for the pure
NJL point. In the nontrivial window the renormalized effective potential yields
a nontrivial interaction which is conformal invariant. The exisitence of the
nontrivial window implies ``cutoff insensitivity'' of the physics prediction in
spite of the ultraviolet dominance of the dynamics. In the formal limit D -> 4,
the nontrivial window coincides with the known condition of the nontriviality
of the four-dimensional gauged NJL model, .Comment: 34 pages, 6 figures, references added, to appear in Phys.Rev.D. The
title is changed in PR
Dynamical Casimir effect in oscillating media
We show that oscillations of a homogeneous medium with constant material
coefficients produce pairs of photons. Classical analysis of an oscillating
medium reveals regions of parametric resonance where the electromagnetic waves
are exponentially amplified. The quantum counterpart of parametric resonance is
an exponentially growing number of photons in the same parameter regions. This
process may be viewed as another manifestation of the dynamical Casimir effect.
However, in contrast to the standard dynamical Casimir effect, photon
production here takes place in the entire volume and is not due to time
dependence of the boundary conditions or material constants
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