7,044 research outputs found
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
Moving boundary approximation for curved streamer ionization fronts: Solvability analysis
The minimal density model for negative streamer ionization fronts is
investigated. An earlier moving boundary approximation for this model consisted
of a "kinetic undercooling" type boundary condition in a Laplacian growth
problem of Hele-Shaw type. Here we derive a curvature correction to the moving
boundary approximation that resembles surface tension. The calculation is based
on solvability analysis with unconventional features, namely, there are three
relevant zero modes of the adjoint operator, one of them diverging;
furthermore, the inner/outer matching ahead of the front has to be performed on
a line rather than on an extended region; and the whole calculation can be
performed analytically. The analysis reveals a relation between the fields
ahead and behind a slowly evolving curved front, the curvature and the
generated conductivity. This relation forces us to give up the ideal
conductivity approximation, and we suggest to replace it by a constant
conductivity approximation. This implies that the electric potential in the
streamer interior is no longer constant but solves a Laplace equation; this
leads to a Muskat-type problem.Comment: 22 pages, 6 figure
Minimal Length and the Quantum Bouncer: A Nonperturbative Study
We present the energy eigenvalues of a quantum bouncer in the framework of
the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum
mechanical and semiclassical schemes. In this paper, we use two equivalent
nonperturbative representations of a deformed commutation relation in the form
[X,P]=i\hbar(1+\beta P^2) where \beta is the GUP parameter. The new
representation is formally self-adjoint and preserves the ordinary nature of
the position operator. We show that both representations result in the same
modified semiclassical energy spectrum and agrees well with the quantum
mechanical description.Comment: 14 pages, 2 figures, to appear in Int. J. Theor. Phy
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
A unified meson-baryon potential
We study the spectra of mesons and baryons, composed of light quarks, in the
framework of a semirelativistic potential model including instanton induced
forces. We show how a simple modification of the instanton interaction in the
baryon sector allows a good description of the meson and the baryon spectra
using an interaction characterized by a unique set of parameters.Comment: 7 figure
Baryon spectra with instanton induced forces
Except the vibrational excitations of and mesons, the main features
of spectra of mesons composed of quarks , , and can be quite well
described by a semirelativistic potential model including instanton induced
forces. The spectra of baryons composed of the same quarks is studied using the
same model. The results and the limitations of this approach are described.
Some possible improvements are suggested.Comment: 5 figure
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