7,274 research outputs found
One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
We present exact energy eigenvalues and eigenfunctions of the one-dimensional
hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty
Principle (GUP). This form of GUP is consistent with various theories of
quantum gravity such as string theory, loop quantum gravity, black-hole
physics, and doubly special relativity and implies a minimal length uncertainty
and a maximal momentum. We show that the quantized energy spectrum exactly
agrees with the semiclassical results.Comment: 10 pages, 1 figur
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
Harmonic oscillator with minimal length uncertainty relations and ladder operators
We construct creation and annihilation operators for harmonic oscillators
with minimal length uncertainty relations. We discuss a possible generalization
to a large class of deformations of cannonical commutation relations. We also
discuss dynamical symmetry of noncommutative harmonic oscillator.Comment: 8 pages, revtex4, final version, to appear in PR
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
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
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