scholarly journals Scattering and Bound States of Duffin-Kemmer-Petiau Particles forq-Parameter Hyperbolic Pöschl-Teller Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hilmi Yanar ◽  
Ali Havare ◽  
Kenan Sogut
Keyword(s):  
Bound States ◽  
Scalar Potential ◽  
Spatial Dimension ◽  
Shape Parameters ◽  
Energy Eigenvalues ◽  
Vector Potentials ◽  
Scattering States ◽  
Potential Shape ◽  
Probability Densities ◽  
Interaction Approach

The Duffin-Kemmer-Petiau (DKP) equation in the presence of a scalar potential is solved in one spatial dimension for the vectorq-parameter Hyperbolic Pöschl-Teller (qHPT) potential. In obtaining complete solutions we used the weak interaction approach and took the scalar and vector potentials in a correlated form. By looking at the asymptotic behaviors of the solutions, we identify the bound and scattering states. We calculate transmission (T) and reflection (R) probability densities and analyze their dependence on the potential shape parameters. Also we investigate the dependence of energy eigenvalues of the bound states on the potential shape parameters.

scholarly journals Approximate treatment of the Dirac equation with scalar and vector potentials of rectangular shapes

2020 ◽  
Vol 4 ◽  
pp. 41
Author(s):  
M. E. Grypeos ◽  
C. G. Koutroulos ◽  
G. J. Papadopoulos
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Scalar Potential ◽  
Particle Energy ◽  
Vector Potentials ◽  
Wide Range ◽  
Analytic Expressions ◽  
Fourth Component ◽  
Approximate Treatment ◽  
Range Of Values

The Dirac equation with scalar potential Us(r) and fourth component of vector po­ tential Uv(r) is considered in the case of the rectangular shapes of these potentials with the same radius R and approximate analytic expressions are derived for the single-particle energy of bound states in certain cases. The results obtained with these expressions are compared with the corresponding "exact" results obtained by solving the eigenvalue equa­ tion numerically.It is found that very good results are obtained for the ground state and for quite a wide range of values of R with one of the proposed expressions. Even the corresponding non-relativistic version of this expession, has not been derived before, to our knowledge.

scholarly journals Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

1985 ◽  
Vol 40 (1) ◽  
pp. 14-28
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Composite Particle ◽  
Composite Particles ◽  
Statistical Interpretation ◽  
Particle Spectrum ◽  
Nonlinear Spinor ◽  
Effective Interactions ◽  
Scattering States ◽  
Diagonal Part

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

scholarly journals The Nonrelativistic Scattering States of the Deng-Fan Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Bentol Hoda Yazarloo ◽  
Liangliang Lu ◽  
Guanghui Liu ◽  
Saber Zarrinkamar ◽  
Hassan Hassanabadi
Keyword(s):  
Approximation Scheme ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Term Energy ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Nonrelativistic Scattering

The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: thel=0and thes-wave Hulthén potential.

Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential

2014 ◽  
Vol 92 (12) ◽  
pp. 1565-1569 ◽  
Author(s):  
M.K. Bahar ◽  
F. Yasuk
Keyword(s):  
Wave Function ◽  
Scalar Potential ◽  
Energy Eigenvalues ◽  
Relativistic Spin ◽  
Ansatz Approach ◽  
Dependent Mass ◽  
Type Potential ◽  
Position Dependent Mass

The relativistic Duffin–Kemmer–Petiau equation for relativistic spin-1 particles with position-dependent mass in the presence of a vector Kratzer-type potential and the absence of a scalar potential is studied analytically. The energy eigenvalues and corresponding eigenfunctions are obtained using the wave function ansatz approach.

scholarly journals Solutions of the Relativistic Two-Body Problem. II. Quantum Mechanics

1972 ◽  
Vol 25 (2) ◽  
pp. 141 ◽  
Author(s):  
JL Cook
Keyword(s):  
Bound States ◽  
Free Particle ◽  
Plane Waves ◽  
Addition Theorem ◽  
Partial Wave Analysis ◽  
Harmonic Oscillator Potential ◽  
Two Body Problem ◽  
Probability Densities ◽  
Square Well ◽  
Potential Harmonic

This paper discusses the formulation of a quantum mechanical equivalent of the relative time classical theory proposed in Part I. The relativistic wavefunction is derived and a covariant addition theorem is put forward which allows a covariant scattering theory to be established. The free particle eigenfunctions that are given are found not to be plane waves. A covariant partial wave analysis is also given. A means is described of converting wavefunctions that yield probability densities in 4-space to ones that yield the 3-space equivalents. Bound states are considered and covariant analogues of the Coulomb potential, harmonic oscillator potential, inverse cube law of force, square well potential, and two-body fermion interactions are discussed.

scholarly journals Mass spectra of heavy pseudoscalars using instantaneous Bethe–Salpeter equation with different kernels

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Wei Li ◽  
Ying-Long Wang ◽  
Tai-Fu Feng ◽  
Guo-Li Wang
Keyword(s):  
Mass Spectra ◽  
Scalar Potential ◽  
Landau Gauge ◽  
Mass Splitting ◽  
Coulomb Gauge ◽  
Exchange Vector ◽  
Feynman Gauge ◽  
Vector Potentials ◽  
Time Component ◽  
Linear Scalar

Abstract We solved the instantaneous Bethe–Salpeter equation for heavy pseudoscalars in different kernels, where the kernels are obtained using linear scalar potential plus one gluon exchange vector potentials in Feynman gauge, Landau gauge, Coulomb gauge and time-component Coulomb gauge. Since we cannot give a complete QCD-based calculation, the results are gauge dependent. We compared the obtained mass spectra of heavy pseudoscalars between different kernels, found that using the same parameters we obtain the smallest mass splitting in time-component Coulomb gauge, the similar largest mass splitting in Feynman and Coulomb gauges, middle size splitting in Landau gauge.

Integrable and chaotic motions of four vortices II. Collision dynamics of vortex pairs

1988 ◽  
Vol 326 (1593) ◽  
pp. 655-696 ◽  
Keyword(s):  
Bound States ◽  
Degrees Of Freedom ◽  
Complex Structure ◽  
Physical Space ◽  
Vantage Point ◽  
Collision Dynamics ◽  
Chaotic Motions ◽  
Vortex Pairs ◽  
Scattering States ◽  
Space Mechanisms

The interaction of two vortex pairs is investigated analytically and by numerical experiments from the vantage point of dynamical-systems theory. Vortex pairs can escape to infinity, so the phase space of this system is unbounded in contrast to that of four identical vortices investigated previously. Chaotic motion is nevertheless possible both for ‘bound states’ of the system and for ‘scattering states’. For the bound states standard Poincare section techniques suffice. For scattering states chaos appears as complex structure in the numerically generated plot of scattering angle against impact parameter. Interpretations of physical space mechanisms leading to chaos are given. Analytical characterizations of the system include a formal reduction to two degrees of freedom by canonical transformations and an identification and discussion of integrable cases of which one is apparently new.

THE ASYMPTOTIC ITERATION METHOD FOR DIRAC AND KLEIN–GORDON EQUATIONS WITH A LINEAR SCALAR POTENTIAL

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4127-4135 ◽  
Author(s):  
T. BARAKAT
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Scalar Potential ◽  
Asymptotic Iteration Method ◽  
Klein Gordon ◽  
Linear Scalar

The asymptotic iteration method is used for Dirac and Klein–Gordon equations with a linear scalar potential to obtain the relativistic eigenenergies. A parameter, ς = 0, 1, is introduced in such a way that one can obtain Klein–Gordon bound states from Dirac bound states. It is shown that this method asymptotically gives accurate results for both Dirac and Klein–Gordon equations.

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.

Sign in / Sign up

Export Citation Format

Share Document