Bound states of the Yukawa potential via the shifted 1/N expansion technique

1984 ◽  
Vol 105 (4-5) ◽  
pp. 183-187 ◽  
Author(s):  
T. Imbo ◽  
A. Pagnamenta ◽  
U. Sukhatme
Keyword(s):  
Bound States ◽  
Yukawa Potential ◽  
Expansion Technique

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

scholarly journals The spinless relativistic Hellmann problem

2019 ◽  
Vol 34 (05) ◽  
pp. 1950028
Author(s):  
Wolfgang Lucha ◽  
Franz F. Schöberl
Keyword(s):  
Coulomb Potential ◽  
Bound States ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Kinetic Term ◽  
Discrete Eigenvalue ◽  
Hellmann Potential ◽  
Relativistic Equations

We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb potential and an either attractive or repulsive Yukawa potential and, hence, generalizations of the Hellmann potential employed in several areas of science. These insights should provide useful guidelines to all attempts of finding appropriate descriptions of bound states by (semi-)relativistic equations of motion.

scholarly journals Bound states and critical behavior of the Yukawa potential

2006 ◽  
Vol 49 (1) ◽  
pp. 60-71 ◽  
Author(s):  
Yongyao Li ◽  
Xiangqian Luo ◽  
Helmut Kröger
Keyword(s):  
Critical Behavior ◽  
Bound States ◽  
Yukawa Potential

scholarly journals SPECTROSCOPY OF Bc MESON IN A SEMI-RELATIVISTIC QUARK MODEL USING THE SHIFTED LARGE-N EXPANSION METHOD

2004 ◽  
Vol 19 (11) ◽  
pp. 1771-1791 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Expansion Method ◽  
The Other ◽  
Minimal Subtraction ◽  
Third Order ◽  
Large N ◽  
Expansion Technique ◽  
Energy Bound ◽  
Bc Meson ◽  
Large N Expansion

We calculate the [Formula: see text] mass spectrum, the splitting values and some other properties in the framework of the semirelativistic equation by applying the shifted large-N expansion technique. We use seven different central potentials together with an improved QCD-motivated interquark potentials calculated to two loops in the modified minimal-subtraction [Formula: see text] scheme. The parameters of these potentials are fitted to generate the semirelativistic bound states of [Formula: see text] quarkonium system in close conformity with the experimental and the present available calculated center-of-gravity (c.o.g.) data. Calculations of the energy bound states are carried out up to third order. Our results are in excellent fit with the results of the other works.

The creation of bound states by a Yukawa potential

1967 ◽  
Vol 50 (2) ◽  
pp. 364-367
Author(s):  
W. J. Abbe
Keyword(s):  
Bound States ◽  
Yukawa Potential ◽  
The Creation

scholarly journals Simple mass estimates for resonance(s) being 6 top + 6 antitop bound states and combinations thereof

2016 ◽  
Vol 31 (32) ◽  
pp. 1650168 ◽  
Author(s):  
H. B. Nielsen
Keyword(s):  
Bound States ◽  
Yukawa Potential ◽  
Simple Calculation ◽  
Bound State ◽  
New Physics ◽  
Step Function ◽  
Multiple Point ◽  
Fundamental Particles ◽  
Simple Mass ◽  
The Masses

We have long speculated,[Formula: see text] that 6 top + 6 antitop quarks due to the relatively large size of the top-Yukawa coupling would bind exceptionally strongly by mainly Higgs exchange. Here we present a surprisingly simple “calculation” of the mass of this speculated bound state. Even a possible resonance in scattering of two such bound states is speculated. For the “calculation” of the masses it is crucial to assume, that our since long speculated principle “multiple point principle,”[Formula: see text] is true. This principle says: there are several vacua all having almost zero energy density. Further, we make an approximation of the Higgs Yukawa potential essentially replacing the exponential in it by a step-function. The new result means that there are now two independent calls for our bound state having the mass around 750 GeV required by our “new law of nature” the Multiple Point Principle. It should be remarked that in our picture there is no new physics in the sense of new fundamental particles, but the “multiple point principle” is new in the sense of being not yet accepted. Further, we get the same mass within uncertainties as earlier2 but now from a completely different assumption, except for being from our “multiple point principle.” But the two masses are gotten from using different (speculative) vacua occurring in the pure Standard Model.

scholarly journals THE SEMIRELATIVISTIC EQUATION VIA THE SHIFTED-l EXPANSION TECHNIQUE

2001 ◽  
Vol 16 (12) ◽  
pp. 2195-2204 ◽  
Author(s):  
T. BARAKAT
Keyword(s):  
Ground State ◽  
Bound States ◽  
Wave Equations ◽  
State Energy ◽  
Wave Functions ◽  
Energy Problem ◽  
Energy Eigenvalues ◽  
Relativistic Corrections ◽  
Expansion Technique ◽  
The Right

The semirelativistic wave equation which appears in the theory of relativistic quark–antiquark bound states, is cast into a constituent second order Schrödinger-like equation with the inclusion of relativistic corrections up to order (v/c)2 in the quarks speeds. The resulting equation is solved via the Shifted-l expansion technique (SLET), which has been recently developed to get eigenvalues and wave functions of relativistic and nonrelativistic wave equations. The Coulomb, Oscillator, and the Coulomb-plus-linear potentials used in [Formula: see text] phenomenology are tested. It is observed that, the energy eigenvalues can be explained well upon the more commonly used nonrelativistic models, when such a dynamical relativistic corrections are introduced. In particular, it provides a remarkable accurate and simple analytic expression for the Coulomb ground-state energy problem, a result which is in the right direction at least to serve as a test of this approach.

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