BOUND STATES BETWEEN TWO PARTICLES IN A TWO- OR THREE-DIMENSIONAL INFINITE LATTICE WITH ATTRACTIVE KRONECKER δ-FUNCTION INTERACTION

1989 ◽  
Vol 03 (10) ◽  
pp. 813-813
Author(s):  
SHAO-JING DONG ◽  
CHEN NING YANG
Keyword(s):  
Wave Function ◽  
Bound States ◽  
State Energy ◽  
Three Dimensional ◽  
Bound State ◽  
Bound State Energy ◽  
3 Dimensional ◽  
Infinite Lattice

The bound state energy and wave function for two particles in a 2- or 3-dimensional infinite lattice with attractive Kronecker δ-function interaction are discussed.

BOUND STATES BETWEEN TWO PARTICLES IN A TWO- OR THREE-DIMENSIONAL INFINITE LATTICE WITH ATTRACTIVE KRONECKER δ-FUNCTION INTERACTION

1989 ◽  
Vol 01 (01) ◽  
pp. 139-146 ◽  
Author(s):  
SHAO-JING DONG ◽  
CHEN NING YANG
Keyword(s):  
Wave Function ◽  
Bound States ◽  
State Energy ◽  
Three Dimensional ◽  
Bound State ◽  
Bound State Energy ◽  
3 Dimensional ◽  
Infinite Lattice

The bound state energy and wave function for two particles in a 2- or 3-dimensional infinite lattice with attractive Kronecker δ-function interaction are discussed.

Bound state energy and wave function of tetraquark b̄b̄ud from lattice QCD potential

2019 ◽  
Vol 34 (27) ◽  
pp. 1950220
Author(s):  
F. Chezani Sharahi ◽  
M. Monemzadeh ◽  
A. Abdoli Arani
Keyword(s):  
Wave Function ◽  
Lattice Qcd ◽  
Bound States ◽  
State Energy ◽  
Energy State ◽  
Light Quark ◽  
Bound State ◽  
Bound State Energy ◽  
Quark System ◽  
Oppenheimer Approximation

In this study, the bound state energy of a four-quark system was analytically calculated as a two heavy–heavy anti-quarks [Formula: see text] and two light–light quarks [Formula: see text]. Tetraquark was assumed to be a bound state of two-body system consisting of two mesons, each containing a light quark and a heavy antiquark. Due to the presence of heavy mesons in the tetraquark, Born–Oppenheimer approximation was used to study its bound states. To assess the bounding energy, Schrödinger equation was solved using lattice QCD [Formula: see text] potential, having expanded the tetraquark potential [Formula: see text] up to 11th term. Binding energy state and wave function, however, were obtained in the scalar [Formula: see text] channel. Graphical results for wave functions obtained versus antiquark–antiquark distance [Formula: see text] confirmed the existence of the tetraquark [Formula: see text]. Analytical bound state energy obtained here was in good agreement with several numerical ones published in the literature, confirming the accuracy of the approach taken here.

scholarly journals Bound states of Newton’s equivalent finite square well

2018 ◽  
Vol 33 (33) ◽  
pp. 1850195
Author(s):  
Amornthep Tita ◽  
Pichet Vanichchapongjaroen
Keyword(s):  
Energy Spectrum ◽  
Bound States ◽  
Infinite Order ◽  
State Energy ◽  
Order Differential Equation ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Standard Quantum ◽  
Square Well

In this paper, a one-parameter family of Newton’s equivalent Hamiltonians (NEH) for finite square well potential is analyzed in order to obtain bound state energy spectrum and wave functions. For a generic potential, each of the NEH is classically equivalent to one another and to the standard Hamiltonian yielding Newton’s equations. Quantum mechanically, however, they are expected to be different from each other. The Schrödinger’s equation coming from each NEH with finite square well potential is an infinite order differential equation. The matching conditions, therefore, demand the wave functions to be infinitely differentiable at the well boundaries. To handle this, we provide a way to consistently truncate these conditions. It turns out as expected that bound state energy spectrum and wave functions are dependent on the parameter [Formula: see text] which is used to characterize different NEH. As [Formula: see text], the energy spectrum coincides with that from the standard quantum finite square well.

Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system

2021 ◽  
Author(s):  
Yi-Cai Zhang
Keyword(s):  
Energy Spectrum ◽  
Continuous Spectrum ◽  
Bound States ◽  
State Energy ◽  
Band System ◽  
Bound State ◽  
Flat Band ◽  
Bound State Energy ◽  
Type Iii ◽  
Potential Strength

Abstract In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength $\alpha$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n, n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength $\alpha_c$ at which the bound state energy reaches the threshold of continuous spectrum. After crossing the threshold, the bound states in the continuum (BIC) would exist in such a flat band system.

scholarly journals Scattering description of Andreev molecules

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Jean-Damien Pillet ◽  
Vincent Benzoni ◽  
Joël Griesmar ◽  
Jean-Loup Smirr ◽  
Çağlar Girit
Keyword(s):  
Bound States ◽  
State Energy ◽  
Bound State ◽  
Transport Processes ◽  
Weak Links ◽  
Bound State Energy ◽  
One Dimensional ◽  
Conduction Channel ◽  
Non Local ◽  
Local Transport

An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local transport processes leading to the formation of Andreev molecules.

Lower Bound for ppK– Quasi-Bound State Energy

2020 ◽  
Vol 51 (5) ◽  
pp. 979-987 ◽  
Author(s):  
I. Filikhin ◽  
B. Vlahovic
Keyword(s):  
Lower Bound ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Quasi Bound State

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Asim Soylu ◽  
Orhan Bayrak ◽  
Ismail Boztosun
Keyword(s):  
Morse Potential ◽  
State Energy ◽  
Bound State ◽  
Quantum States ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Dependent Term ◽  
Oscillator Type ◽  
Dependent Potential ◽  
Pekeris Approximation

AbstractWe investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ 0, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ 0 r 2, we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ 0, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.

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.

scholarly journals ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL

2010 ◽  
Vol 19 (07) ◽  
pp. 1463-1475 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
S. V. BADALOV
Keyword(s):  
State Energy ◽  
Gordon Equation ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Saxon Potential ◽  
Bound State Energy ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Pekeris Approximation ◽  
Klein Gordon Equation

The radial part of the Klein–Gordon equation for the Woods–Saxon potential is solved. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for any l-states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers n and l. The nonrelativistic limit of the bound state energy spectrum was also found.

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