7,374 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
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
Comment on `Glueball spectrum from a potential model'
In a recent article, W.-S. Hou and G.-G. Wong [Phys. Rev. D {\bf 67}, 034003
(2003)] have investigated the spectrum of two-gluon glueballs below 3 GeV in a
potential model with a dynamical gluon mass. We point out that, among the 18
states calculated by the authors, only three are physical. The other states
either are spurious or possess a finite mass only due to an arbitrary
restriction of the variational parameter.Comment: Comment on pape
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
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
Electromagnetic splitting for mesons and baryons using dressed constituent quarks
Electromagnetic splittings for mesons and baryons are calculated in a
formalism where the constituent quarks are considered as dressed
quasiparticles. The electromagnetic interaction, which contains coulomb,
contact, and hyperfine terms, is folded with the quark electrical density. Two
different types of strong potentials are considered. Numerical treatment is
done very carefully and several approximations are discussed in detail. Our
model contains only one free parameter and the agreement with experimental data
is reasonable although it seems very difficult to obtain a perfect description
in any case.Comment: 14 pages, Revised published versio
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
On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
Different candidates of Quantum Gravity such as String Theory, Doubly Special
Relativity, Loop Quantum Gravity and black hole physics all predict the
existence of a minimum observable length or a maximum observable momentum which
modifies the Heisenberg uncertainty principle. This modified version is usually
called the Generalized (Gravitational) Uncertainty Principle (GUP) and changes
all Hamiltonians in quantum mechanics. In this Letter, we use a recently
proposed GUP which is consistent with String Theory, Doubly Special Relativity
and black hole physics and predicts both a minimum measurable length and a
maximum measurable momentum. This form of GUP results in two additional terms
in any quantum mechanical Hamiltonian, proportional to and
, respectively, where is the GUP
parameter. By considering both terms as perturbations, we study two quantum
mechanical systems in the framework of the proposed GUP: a particle in a box
and a simple harmonic oscillator. We demonstrate that, for the general
polynomial potentials, the corrections to the highly excited eigenenergies are
proportional to their square values. We show that this result is exact for the
case of a particle in a box.Comment: 11 pages, to appear in Europhysics Letter
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
Minimal Length Uncertainty Relation and gravitational quantum well
The dynamics of a particle in a gravitational quantum well is studied in the context of nonrelativistic quantum mechanics with a particular deformation of a two-dimensional Heisenberg algebra. This deformation yields a new short-distance structure characterized by a finite minimal uncertainty in position measurements, a feature it shares with noncommutative theories. We show that an analytical solution can be found in perturbation and we compare our results to those published recently, where noncommutative geometry at the quantum mechanical level was considered. We find that the perturbations of the gravitational quantum well spectrum in these two approaches have different signatures. We also compare our modified energy spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultra cold neutrons moving above a mirror are studied. This comparison leads to an upper bound on the minimal length scale induced by the deformed algebra we use. This upper bound is weaker than the one obtained in the context of the hydrogen atom but could still be useful if the deformation parameter of the Heisenberg algebra is not a universal constant but a quantity that depends on the energetic content of the system
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