7,043 research outputs found

### Upper and lower bounds on the mean square radius and criteria for occurrence of quantum halo states

In the context of non-relativistic quantum mechanics, we obtain several upper
and lower limits on the mean square radius applicable to systems composed by
two-body bound by a central potential. A lower limit on the mean square radius
is used to obtain a simple criteria for the occurrence of S-wave quantum halo
sates.Comment: 12 pages, 2 figure

### Analytical Solution of the Relativistic Coulomb Problem with a Hard-Core Interaction for a One-Dimensional Spinless Salpeter Equation

In this paper, we construct an analytical solution of the one-dimensional spinless Salpeter equation with a Coulomb potential supplemented by a hard core interaction, which keeps the particle in the x positive region

### Bohr-Sommerfeld quantization and meson spectroscopy

We use the Bohr-Sommerfeld quantization approach in the context of
constituent quark models. This method provides, for the Cornell potential,
analytical formulae for the energy spectra which closely approximate numerical
exact calculations performed with the Schrodinger or the spinless Salpeter
equations. The Bohr-Sommerfeld quantization procedure can also be used to
calculate other observables such as r.m.s. radius or wave function at the
origin. Asymptotic dependence of these observables on quantum numbers are also
obtained in the case of potentials which behave asymptotically as a power-law.
We discuss the constraints imposed by these formulae on the dynamics of the
quark-antiquark interaction.Comment: 13 page

### One dimensional Coulomb-like problem in deformed space with minimal length

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb
potential with deformed Heisenberg algebra leading to minimal length are found
exactly. It is shown that correction due to the deformation is proportional to
square root of the deformation parameter. We obtain the same spectrum using
Bohr-Sommerfeld quantization condition.Comment: 11 pages, typos corrected, references adde

### Necessary and sufficient conditions for existence of bound states in a central potential

We obtain, using the Birman-Schwinger method, a series of necessary
conditions for the existence of at least one bound state applicable to
arbitrary central potentials in the context of nonrelativistic quantum
mechanics. These conditions yield a monotonic series of lower limits on the
"critical" value of the strength of the potential (for which a first bound
state appears) which converges to the exact critical strength. We also obtain a
sufficient condition for the existence of bound states in a central monotonic
potential which yield an upper limit on the critical strength of the potential.Comment: 7 page

### Critical strength of attractive central potentials

We obtain several sequences of necessary and sufficient conditions for the
existence of bound states applicable to attractive (purely negative) central
potentials. These conditions yields several sequences of upper and lower limits
on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant
(strength), $g$, of the potential, $V(r)=-g v(r)$, for which a first
$\ell$-wave bound state appears, which converges to the exact critical value.Comment: 18 page

### Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition

Successful applications of the Kruskal-Segur approach to interfacial pattern
formation have remained limited due to the necessity of an integral formulation
of the problem. This excludes nonlinear bulk equations, rendering convection
intractable. Combining the method with Zauderer's asymptotic decomposition
scheme, we are able to strongly extend its scope of applicability and solve
selection problems based on free boundary formulations in terms of partial
differential equations alone. To demonstrate the technique, we give the first
analytic solution of the problem of velocity selection for dendritic growth in
a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page

### Broadband optical gain via interference in the free electron laser: principles and proposed realizations

We propose experimentally simplified schemes of an optically dispersive
interface region between two coupled free electron lasers (FELs), aimed at
achieving a much broader gain bandwidth than in a conventional FEL or a
conventional optical klystron composed of two separated FELs. The proposed
schemes can {\it universally} enhance the gain of FELs, regardless of their
design when operated in the short pulsed regime

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