7,738 research outputs found
Upper limit on the critical strength of central potentials in relativistic quantum mechanics
In the context of relativistic quantum mechanics, where the Schr\"odinger
equation is replaced by the spinless Salpeter equation, we show how to
construct a large class of upper limits on the critical value,
, of the coupling constant, , of the central potential,
. This critical value is the value of for which a first
-wave bound state appears.Comment: 8 page
A semiclassical model of light mesons
The dominantly orbital state description is applied to the study of light
mesons. The effective Hamiltonian is characterized by a relativistic kinematics
supplemented by the usual funnel potential with a mixed scalar and vector
confinement. The influence of two different finite quark masses and potential
parameters on Regge and vibrational trajectories is discussed.Comment: 1 figur
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
Sufficient conditions for the existence of bound states in a central potential
We show how a large class of sufficient conditions for the existence of bound
states, in non-positive central potentials, can be constructed. These
sufficient conditions yield upper limits on the critical value,
, of the coupling constant (strength), , of the
potential, , for which a first -wave bound state appears.
These upper limits are significantly more stringent than hitherto known
results.Comment: 7 page
Renormalization of the singular attractive potential
We study the radial Schr\"odinger equation for a particle of mass in the
field of a singular attractive potential with particular emphasis
on the bound states problem. Using the regularization method of Beane
\textit{et al.}, we solve analytically the corresponding ``renormalization
group flow" equation. We find in agreement with previous studies that its
solution exhibits a limit cycle behavior and has infinitely many branches. We
show that a continuous choice for the solution corresponds to a given fixed
number of bound states and to low energy phase shifts that vary continuously
with energy. We study in detail the connection between this regularization
method and a conventional method modifying the short range part of the
potential with an infinitely repulsive hard core. We show that both methods
yield bound states results in close agreement even though the regularization
method of Beane \textit{et al.} does not include explicitly any new scale in
the problem. We further illustrate the use of the regularization method in the
computation of electron bound states in the field of neutral polarizable
molecules without dipole moment. We find the binding energy of s-wave
polarization bound electrons in the field of C molecules to be 17 meV
for a scattering length corresponding to a hard core radius of the size of the
molecule radius ( \AA). This result can be further compared with
recent two-parameter fits using the Lennard-Jones potential yielding binding
energies ranging from 3 to 25 meV.Comment: 8 page
Radiative diagnostics for sub-Larmor scale magnetic turbulence
Radiative diagnostics of high-energy density plasmas is addressed in this
paper. We propose that the radiation produced by energetic particles in
small-scale magnetic field turbulence, which can occur in laser-plasma
experiments, collisionless shocks, and during magnetic reconnection, can be
used to deduce some properties of the turbulent magnetic field. Particles
propagating through such turbulence encounter locally strong magnetic fields,
but over lengths much shorter than a particle gyroradius. Consequently, the
particle is accelerated but not deviated substantially from a straight line
path. We develop the general jitter radiation solutions for this case and show
that the resulting radiation is directly dependent upon the spectral
distribution of the magnetic field through which the particle propagates. We
demonstrate the power of this approach in considering the radiation produced by
particles moving through a region in which a (Weibel-like) filamentation
instability grows magnetic fields randomly oriented in a plane transverse to
counterstreaming particle populations. We calculate the spectrum as would be
seen from the original particle population and as could be seen by using a
quasi-monoenergetic electron beam to probe the turbulent region at various
angles to the filamentation axis.Comment: 17 pages, 4 figures, submitted to Phys. Plasma
Universality of Regge and vibrational trajectories in a semiclassical model
The orbital and radial excitations of light-light mesons are studied in the
framework of the dominantly orbital state description. The equation of motion
is characterized by a relativistic kinematics supplemented by the usual funnel
potential with a mixed scalar and vector confinement. The influence of finite
quark masses and potential parameters on Regge and vibrational trajectories is
discussed. The case of heavy-light mesons is also presented.Comment: 12 page
A mass formula for light mesons from a potential model
The quark dynamics inside light mesons, except pseudoscalar ones, can be
quite well described by a spinless Salpeter equation supplemented by a Cornell
interaction (possibly partly vector, partly scalar). A mass formula for these
mesons can then be obtained by computing analytical approximations of the
eigenvalues of the equation. We show that such a formula can be derived by
combining the results of two methods: the dominantly orbital state description
and the Bohr-Sommerfeld quantization approach. The predictions of the mass
formula are compared with accurate solutions of the spinless Salpeter equation
computed with a Lagrange-mesh calculation method.Comment: 5 figure
Microfinance: A Comprehensive Review of the Existing Literature
Although the word finance is in the term microfinance, and the core elements of microfinance are those of the finance discipline, microfinance has yet to break into the mainstream or entrepreneurial finance literature. The purpose of this article is to introduce the finance academic community to the discipline of microfinance and microfinance institutions (MFIs). We provide a comprehensive review of over 350 articles and address the issues of MFI sustainability, products and services, management practices, clientele targeting, regulation and policy, and impact assessment
Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length
An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the
Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is
considered from the perspective of the radial Schr\"odinger equations on 3D
spaces of any (either positive, zero or negative) constant curvature. Further
to Stevenson, we show in detail how to get the hypergeometric wavefunction for
the hydrogen atom case. Finally, we make a comparison between the ``space
curvature" effects and minimal length effects for the hydrogen spectrumComment: 6 pages, v
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