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

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x12501618 ◽

2012 ◽

Vol 27 (27) ◽

pp. 1250161 ◽

Cited By ~ 9

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.

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An introduction to the inverse quantum bound-state problem in one dimension

American Journal of Physics ◽

10.1119/1.4868335 ◽

2014 ◽

Vol 82 (7) ◽

pp. 674-680

Author(s):

Thomas D. Gutierrez

Keyword(s):

Bound State ◽

One Dimension ◽

State Problem ◽

Bound State Problem

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Bound States in Two-dimensional Crossed or Bent Quantum Wires

International Journal of Modern Physics B ◽

10.1142/s0217979298001101 ◽

1998 ◽

Vol 12 (19) ◽

pp. 1907-1919 ◽

Cited By ~ 2

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.

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

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817500116 ◽

2016 ◽

Vol 14 (01) ◽

pp. 1750011 ◽

Cited By ~ 2

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].

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