A simple analytical expression for bound state energies for an attractive Gaussian confining potential

2012 ◽  
Vol 86 (3) ◽  
pp. 035006 ◽  
Author(s):  
K Köksal
Keyword(s):  
Bound State ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
Confining Potential

scholarly journals BEST SEPARABLE APPROXIMATION WITH SEMI-DEFINITE PROGRAMMING METHOD

2004 ◽  
Vol 02 (04) ◽  
pp. 541-558 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MIRZAEE ◽  
M. REZAEE
Keyword(s):  
Mixed State ◽  
Qubit State ◽  
Programming Method ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
Isotropic State ◽  
Separable Approximation ◽  
Isotropic States

The present methods for obtaining the optimal Lewenestein–Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein–Sanpera decomposition by using semi-definite programming. In particular, we obtain the optimal Lewenstein–Sanpera decomposition for some examples such as: the Bell decomposable state, the iso-concurrence state, the generic two-qubit state in the Wootters basis, the 2⊗3 Bell decomposable state, the d⊗d Werner and isotropic states, a one parameter 3⊗3 state, and finally a multi-partite isotropic state.

ON T-VIOLATION IN MATTER NEUTRINO OSCILLATIONS

1991 ◽  
Vol 06 (06) ◽  
pp. 455-460 ◽  
Author(s):  
S. TOSHEV
Keyword(s):  
Neutrino Oscillations ◽  
Measurable Quantity ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
T Violation

We continue the investigation of possible T-violating effects in three-neutrino oscillations in matter. Intriguingly simple analytical expression for the experimentally measurable quantity [Formula: see text] (t) is derived.

THE BOUND STATE EQUATION FOR TWO GLUONS AND ITS SOLUTION

1999 ◽  
Vol 14 (13) ◽  
pp. 2117-2132
Author(s):  
J. Y. CUI ◽  
J. M. WU
Keyword(s):  
Field Theory ◽  
Relativistic Quantum ◽  
Bound State ◽  
State Equation ◽  
Exchange Potential ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Lattice Calculation ◽  
Confining Potential ◽  
Instantaneous Approximation

We derive the bound state equation for two gluons in relativistic quantum field theory, i.e. the Bethe–Salpeter (BS) equation for two gluons. To solve it, we choose the kernel as the sum of a one-gluon exchange potential, a contact interaction and a linear confining potential. Under instantaneous approximation, this BS equation is solved numerically. The spectrum and the BS wave function of the glueballs are obtained in this framework. The numerical results are in agreement with that of recent lattice calculation.

scholarly journals MASS SPECTRUM OF THE JP=1/2- AND 3/2- PENTAQUARK ANTIDECUPLETS IN THE PERTURBATIVE CHIRAL QUARK MODEL

2005 ◽  
Vol 14 (07) ◽  
pp. 995-1015 ◽  
Author(s):  
T. INOUE ◽  
V. E. LYUBOVITSKIJ ◽  
TH. GUTSCHE ◽  
AMAND FAESSLER
Keyword(s):  
Mass Spectrum ◽  
Quark Model ◽  
Single Particle ◽  
Ground State ◽  
Bound State ◽  
Wave Functions ◽  
Chiral Quark Model ◽  
Confining Potential ◽  
Full Mass Spectrum ◽  
Basic Configuration

We study the recently discovered Θ+ baryon in the context of the perturbative chiral quark model. The basic configuration of the Θ+ is a pentaquark bound state, where the single particle wave functions are the ground state solutions of a confining potential. We classify the resulting pentaquark multiplets as the JP=1/2- and 3/2- flavor SU (3) antidecuplet. The full mass spectrum of the multiplets is determined by including the meson and gluon cloud contributions, which induce flavor SU (3) breaking. The resulting 3/2- antidecuplet is about 185 MeV heavier than the 1/2- one, mainly because of the semi-perturbative gluon effects. We assign the observed Θ+ baryon as a member of the 1/2- antidecuplet and discuss in particular its relation to the recent experimental signal for a Ξ-- baryon.

The formation of a dip on the surface of a liquid draining from a tank

1967 ◽  
Vol 29 (2) ◽  
pp. 385-390 ◽  
Author(s):  
Barry T. Lubin ◽  
George S. Springer
Keyword(s):  
Experimental Data ◽  
Liquid Surface ◽  
Cylindrical Tank ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
Stationary Liquid ◽  
Circular Orifice ◽  
Good Agreement

Experiments were performed studying the formation of a dip on the surface of an initially stationary liquid draining from a cylindrical tank through an axisym-metrically placed circular orifice. Based upon the information obtained from the experiments, a simple analytical expression was derived predicting the height of the liquid surface in the tank at which this dip forms. A comparison was made between the experimental data and the results of the analysis and good agreement was found between theory and data.

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