6,531 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,
$g_{\rm{c}}^{(\ell)}$, of the coupling constant, $g$, of the central potential,
$V(r)=-g v(r)$. This critical value is the value of $g$ for which a first
$\ell$-wave bound state appears.Comment: 8 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,
$g_{\rm{c}}^{(\ell)}$, of the coupling constant (strength), $g$, of the
potential, $V(r)=-g v(r)$, for which a first $\ell$-wave bound state appears.
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 $-\alpha
r^\lambda \exp(-\beta r)$ 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 $\alpha p^3$ and
$\alpha^2 p^4$, respectively, where $\alpha \sim 1/M_{Pl}c$ 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

### 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

### Renormalization of the singular attractive $1/r^4$ potential

We study the radial Schr\"odinger equation for a particle of mass $m$ in the
field of a singular attractive $g^2/{r^4}$ 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$_{60}$ molecules to be 17 meV
for a scattering length corresponding to a hard core radius of the size of the
molecule radius ($\sim 3.37$ \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

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