scholarly journals On the number of bound states of point interactions on hyperbolic manifolds

2016 ◽  
Vol 14 (01) ◽  
pp. 1750011 ◽  
Author(s):  
Fatih Erman
Keyword(s):  
Riemannian Manifolds ◽  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Hyperbolic Manifolds ◽  
Point Interactions ◽  
State Problem ◽  
Relativistic Extension ◽  
Bound State Problem ◽  
Attractive Point

We study the bound state problem for [Formula: see text] attractive point Dirac [Formula: see text]-interactions in two- and three-dimensional Riemannian manifolds. We give a sufficient condition for the Hamiltonian to have [Formula: see text] bound states and give an explicit criterion for it in hyperbolic manifolds [Formula: see text] and [Formula: see text]. Furthermore, we study the same spectral problem for a relativistic extension of the model on [Formula: see text] and [Formula: see text].

scholarly journals POSSIBLE $D\bar{D}$ AND $B\bar{B}$ MOLECULAR STATES IN A CHIRAL QUARK MODEL

2012 ◽  
Vol 27 (27) ◽  
pp. 1250161 ◽  
Author(s):  
M. T. LI ◽  
W. L. WANG ◽  
Y. B. DONG ◽  
Z. Y. ZHANG
Keyword(s):  
Quark Model ◽  
Systematic Study ◽  
Bound States ◽  
Effective Interaction ◽  
Bound State ◽  
Chiral Quark Model ◽  
State Problem ◽  
Bound State Problem

We perform a systematic study of the bound state problem of [Formula: see text] and [Formula: see text] systems by using effective interaction in our chiral quark model. Our results show that both the interactions of [Formula: see text] and [Formula: see text] states are attractive, which consequently result in [Formula: see text] and [Formula: see text] bound states.

Bound States in Two-dimensional Crossed or Bent Quantum Wires

1998 ◽  
Vol 12 (19) ◽  
pp. 1907-1919 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Conformal Transformation ◽  
Bound States ◽  
Dirichlet Boundary ◽  
Quantum Wires ◽  
Bound State ◽  
Two Dimensional ◽  
State Problem ◽  
Bound State Problem ◽  
Energy Dependent ◽  
Sharp Corners

The method of conformal transformation is applied to solve the bound state problem for two-dimensional crossed wires with sharp and with smooth circular corners, for T-shaped and L-shaped wires and a number of other geometries. It is shown that in this method the wave equation with Dirichlet boundary condition on the boundaries of these wires can be transformed to a Schrödinger equation with a unique two-dimensional energy-dependent noneseparable potential. The results for various geometries indicate that sharp corners are essential in generating the bound states.

On the number of bound states of semirelativistic Hamiltonian with Dirac delta potentials in one dimension

2018 ◽  
Vol 96 (11) ◽  
pp. 1235-1241
Author(s):  
Fatih Erman
Keyword(s):  
Bound States ◽  
Bound State ◽  
One Dimension ◽  
Sufficient Condition ◽  
Explicit Criterion ◽  
State Problem ◽  
Dirac Delta ◽  
Bound State Problem

We study the bound state problem for semirelativistic N attractive Dirac δ-potentials in one dimension. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it.

Singular integral equations in the bound-state problem

1965 ◽  
Vol 35 (3) ◽  
pp. 913-932 ◽  
Author(s):  
G. Cosenza ◽  
L. Sertorio ◽  
M. Toller
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Bound State ◽  
State Problem ◽  
Bound State Problem

Bound-state problem of theNΔandNΔΔsystems

1999 ◽  
Vol 59 (1) ◽  
pp. 46-52 ◽  
Author(s):  
R. D. Mota ◽  
A. Valcarce ◽  
F. Fernández ◽  
H. Garcilazo
Keyword(s):  
Bound State ◽  
State Problem ◽  
Bound State Problem

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

THE NEXT STEP IN LEPTONIC DECAYS OF ETA AND KL BOUND STATES

1992 ◽  
Vol 07 (09) ◽  
pp. 1935-1951 ◽  
Author(s):  
G.A. KOZLOV
Keyword(s):  
Field Theory ◽  
Transition Form Factor ◽  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Quantum Field ◽  
Relative Momentum ◽  
Transition Form ◽  
Structure Transition ◽  
Leptonic Decays

A systematic discussion of the probability of eta and KL bound-state decays—[Formula: see text] and [Formula: see text](l=e, μ)—within a three-dimensional reduction to the two-body quantum field theory is presented. The bound-state vertex function depends on the relative momentum of constituent-like particles. A structure-transition form factor is defined by a confinement-type quark-antiquark wave function. The phenomenology of this kind of decays is analyzed.

scholarly journals Note on the Bound State Problem

1955 ◽  
Vol 13 (3) ◽  
pp. 338-340
Author(s):  
Takao Okabayashi
Keyword(s):  
Bound State ◽  
State Problem ◽  
Bound State Problem
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