7,428 research outputs found
Scattering solutions of the spinless Salpeter equation
A method to compute the scattering solutions of a spinless Salpeter equation
(or a Schrodinger equation) with a central interaction is presented. This
method relies on the 3-dimensional Fourier grid Hamiltonian method used to
compute bound states. It requires only the evaluation of the potential at
equally spaced grid points and yields the radial part of the scattering
solution at the same grid points. It can be easily extended to the case of
coupled channel equations and to the case of non-local interactions.Comment: 7 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
How Geometry Controls the Tearing of Adhesive Thin Films on Curved Surfaces
Flaps can be detached from a thin film glued on a solid substrate by tearing
and peeling. For flat substrates, it has been shown that these flaps
spontaneously narrow and collapse in pointy triangular shapes. Here we show
that various shapes, triangular, elliptic, acuminate or spatulate, can be
observed for the tears by adjusting the curvature of the substrate. From
combined experiments and theoretical models, we show that the flap morphology
is governed by simple geometric rules.Comment: 6 pages, 5 figure
Comment on "Quantum mechanics of smeared particles"
In a recent article, Sastry has proposed a quantum mechanics of smeared
particles. We show that the effects induced by the modification of the
Heisenberg algebra, proposed to take into account the delocalization of a
particle defined via its Compton wavelength, are important enough to be
excluded experimentally.Comment: 2 page
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
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
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, , of the coupling constant
(strength), , of the potential, , for which a first
-wave bound state appears, which converges to the exact critical value.Comment: 18 page
Minimal Length Uncertainty Relation and Hydrogen Atom
We propose a new approach to calculate perturbatively the effects of a
particular deformed Heisenberg algebra on energy spectrum. We use this method
to calculate the harmonic oscillator spectrum and find that corrections are in
agreement with a previous calculation. Then, we apply this approach to obtain
the hydrogen atom spectrum and we find that splittings of degenerate energy
levels appear. Comparison with experimental data yields an interesting upper
bound for the deformation parameter of the Heisenberg algebra.Comment: 7 pages, REVTe
On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions
The Dirac equation has been studied in which the Dirac matrices
\hat{\boldmath\alpha}, \hat\beta have space factors, respectively and
, dependent on the particle's space coordinates. The function deforms
Heisenberg algebra for the coordinates and momenta operators, the function
being treated as a dependence of the particle mass on its position. The
properties of these functions in the transition to the Schr\"odinger equation
are discussed. The exact solution of the Dirac equation for the particle motion
in the Coulomnb field with a linear dependence of the function on the
distance to the force centre and the inverse dependence on for the
function has been found.Comment: 13 page
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