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.

Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

2015 ◽  
Vol 70 (7) ◽  
pp. 499-505 ◽  
Author(s):  
Zahra Sharifi ◽  
Fateme Tajic ◽  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Wave Function ◽  
Magnetic Fields ◽  
Ground State ◽  
Bound States ◽  
State Energy ◽  
Potential Model ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Ansatz Method

AbstractThe Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

SEMI-RELATIVISTIC SOLUTIONS OF THE TWO-BODY SPINLESS SALPETER EQUATION UNDER THE WOODS–SAXON POTENTIAL AND THE PEKERIS APPROXIMATION

2013 ◽  
Vol 22 (06) ◽  
pp. 1350039 ◽  
Author(s):  
H. FEIZI ◽  
M. HOSEININAVEH ◽  
A. H. RANJBAR
Keyword(s):  
Particle Physics ◽  
Nuclear Physics ◽  
Bound States ◽  
State Energy ◽  
Bound State ◽  
Wave Functions ◽  
Shape Invariance ◽  
Energy Eigenvalues ◽  
Elementary Particle Physics ◽  
Pekeris Approximation

In this paper, by applying the Pekeris approximation and in the frame of Supersymmetric Quantum Mechanics (SUSYQM), the semi-relativistic solutions of the two-body spinless Salpeter equation are obtained analytically. For an interaction of nuclear form, we obtain the approximate bound-state energy eigenvalues and the corresponding wave functions using the shape invariance concept. The solutions are reported for any l state and some energy eigenvalues are given. These results are useful in elementary-particle physics and nuclear physics to obtain the bound states spectra of relativistic systems such as fermion–antifermion systems.

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

Dirac Equation with Mixed Scalar–Vector–Pseudoscalar Linear Potential under Relativistic Symmetries

2015 ◽  
Vol 70 (9) ◽  
pp. 713-720 ◽  
Author(s):  
Hadi Tokmehdashi ◽  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Wave Functions ◽  
Linear Potential ◽  
Energy Eigenvalues ◽  
Nu Method

AbstractIn the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation, which describes the motion of a spin-1/2 particle in 1+1 dimensions for mixed scalar–vector–pseudoscalar linear potential are investigated. The Nikiforov–Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms.

scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

Three-Spin-Polarons and Their Elastic Interaction in Cuprates

2003 ◽  
Vol 17 (10n12) ◽  
pp. 415-421 ◽  
Author(s):  
B. I. Kochelaev ◽  
A. M. Safina ◽  
A. Shengelaya ◽  
H. Keller ◽  
K. A. Müller ◽  
...  
Keyword(s):  
Phase Separation ◽  
Ground State ◽  
State Energy ◽  
Elastic Interaction ◽  
Wave Functions ◽  
Extended Hubbard Model ◽  
Phonon Coupling ◽  
Phonon Field ◽  
Oxygen Hole ◽  
Spin Polarons

Properties of quasiparticles in doped cuprates formed by an oxygen hole and two adjacent copper holes are investigated on the basis of the extended Hubbard model. The ground state energy, wave functions and the polaron-phonon coupling are calculated. We also analyzed the polaron-polaron interaction via the phonon field. It was found that this interaction is highly anisotropic and can explain the experimentally observed phase separation in the strongly underdoped LaSrCuO:Mn system.

scholarly journals Solution of The Schrödinger Equation for Trigonometric Scarf Plus Poschl-Teller Non-Central Potential Using Supersymmetry Quantum Mechanics

2016 ◽  
Vol 4 (01) ◽  
pp. 1 ◽  
Author(s):  
Cari C ◽  
Suparmi S ◽  
Antomi Saregar
Keyword(s):  
Ground State ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
State Wave ◽  
Shape Invariant ◽  
Raising Operator ◽  
Invariant Properties ◽  
Lowering Operator ◽  
Exact Energy

<span>In this paper, we show that the exact energy eigenvalues and eigen functions of the Schrödinger <span>equation for charged particles moving in certain class of noncentral potentials can be easily <span>calculated analytically in a simple and elegant manner by using Supersymmetric method <span>(SUSYQM). We discuss the trigonometric Scarf plus Poschl-Teller systems. Then, by operating <span>the lowering operator we get the ground state wave function, and the excited state wave functions <span>are obtained by operating raising operator repeatedly. The energy eigenvalue is expressed in the <span>closed form obtained using the shape invariant properties. The results are in exact agreement with <span>other methods.</span></span></span></span></span></span></span><br /></span>

Single-centre expansions for the hydrogen molecular ion. II

1962 ◽  
Vol 58 (1) ◽  
pp. 130-135 ◽  
Author(s):  
M. Cohen
Keyword(s):  
Ground State ◽  
State Energy ◽  
Internuclear Separation ◽  
Single Centre ◽  
Eigenvalues And Eigenfunctions ◽  
Exact Wave Function ◽  
Radial Functions ◽  
Energy Eigenvalues ◽  
Energy Eigenvalues And Eigenfunctions ◽  
Good Agreement

In an earlier paper (Cohen and Coulson(3), referred to hereafter as I), it was shown that satisfactory energy eigenvalues and eigenfunctions for various even σ-states of may be obtained using a single-centre expansion, provided that the radial functions are properly determined. In particular, the ground-state energy at the equilibrium internuclear separation of 2 a.u. was found to be within 0·25% of the exact value (Bates, Ledsham and Stewart (2)), and the eigenfunction reproduced all the characteristics of the exact wave-function. The method has now been extended to the odd σ-states, as well as to the two lowest π-states (2pπu, 3dπg), and the results are in good agreement with the calculations of Bates et al.

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