A method is presented that allows to solve the Faddeev integral equations of the semirelativistic constituent quark model. In such a model the quark-quark interaction is modeled by a infinitely rising confining potential and the kinetic energy is taken in a relativistic form. We solve the integral equations in Coulomb-Sturmian basis. This basis facilitate an exact treatment of the confining potentials.
The hydrodynamic behavior observed for a sphere released under gravity in a Newtonian liquid is not consistent with that predicted by classical continuum theory when the sphere is near a solid wall. An irreversibility arises in the velocity of the sphere as it approaches and recedes from the plane that cannot be accounted for using continuum hydrodynamic equations alone. Earlier experiments on spheres falling from a plane were conducted under conditions such that this irreversibility could be attributed to the surface roughness of the spheres. In this investigation, we extend these studies to situations where the pressure field between the receding sphere and the plane drops to the vapor pressure of the fluid and cavitation occurs. Experimental data supports the theoretical prediction for a sphere's motion based on the irreversible effect of cavitation.
A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional shortrange terms are expanded in a Coulomb-Sturmian basis. Such kinds of Hamiltonians are frequently used in atomic, nuclear, and particle physics.Keywords Relativistic quantum mechanics · Confining potentials · Meson spectra 1 IntroductionNon-relativistic and semi-relativistic Hamiltonians with infinitely rising potentials are often used to model quark-quark interactions or other quantum particles in a trap. There are many methods for solving the Schrödinger equation with these kinds of potentials. They mostly rely on variational principles and can provide satisfactory results for the few lowest-lying states. However, they are unable to account for the most important property of the system; they cannot grasp the infinitely many bound states, which can be important if we want to consider three or more particles.In this paper we offer a method that can provide an exact treatment of the infinitely rising confinement potentials. We consider both non-relativistic and semi-relativistic kinetic energy with linear and quadratic confinement. We write the bound-state problem in integral equation form and incorporate the kinetic energy and the confining terms into the Green's operator. Then we perform a separable expansion of the shortrange terms in the Coulomb-Sturmian basis. This basis allows an exact evaluation of the Green's operator in terms of continued fractions and provides an asymptotically exact treatment of problems with linear and quadratic confinement.
By solving the Faddeev equations we calculate the mass of the strange baryons in the framework of a relativistic constituent quark model. The Goldstone-boson-exchange quark-quark interaction is derived from SU (3)F symmetry, which is explicitly broken as the strange quark is much heavier. This broken symmetry can nicely be accounted for in the Faddeev framework.
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