Scattering states of the Klein–Gordon equation with Coulomb-like scalar plus vector potentials in arbitrary dimension

2004 ◽  
Vol 330 (6) ◽  
pp. 424-428 ◽  
Author(s):  
Chang-Yuan Chen ◽  
Dong-Sheng Sun ◽  
Fa-Lin Lu
Keyword(s):  
Gordon Equation ◽  
Arbitrary Dimension ◽  
Vector Potentials ◽  
Scattering States ◽  
Klein Gordon ◽  
Klein Gordon Equation

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

THE RELATIVISTIC BOUND AND SCATTERING STATES OF THE ECKART POTENTIAL WITH A PROPER NEW APPROXIMATE SCHEME FOR THE CENTRIFUGAL TERM

2009 ◽  
Vol 24 (01) ◽  
pp. 161-172 ◽  
Author(s):  
GAO-FENG WEI ◽  
SHI-HAI DONG ◽  
V. B. BEZERRA
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Scattering Amplitude ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Klein Gordon ◽  
Klein Gordon Equation

The approximately analytical bound and scattering state solutions of the arbitrary l wave Klein–Gordon equation for mixed Eckart potentials are obtained through a proper new approximation to the centrifugal term. The normalized analytical radial wave functions of the l wave Klein–Gordon equation with the mixed Eckart potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Two special cases — for the s wave and for l = 0 and β = 0 — are also studied, briefly.

scholarly journals The Klein-Gordon equation with the Kratzer potential in d dimensions

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Nasser Saad ◽  
Richard Hall ◽  
Hakan Ciftci
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Monic Polynomial ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Vector Potentials ◽  
Klein Gordon ◽  
Elementary Symmetric Polynomials ◽  
Potential Parameters ◽  
Klein Gordon Equation

AbstractWe apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r) = V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Gao-Feng Wei ◽  
Zhi-Zhong Zhen ◽  
Shi-Hai Dong
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Scattering Amplitude ◽  
Energy Levels ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Scattering States ◽  
Scattering State ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractThe approximately analytical bound and scattering state solutions of the arbitrary l-wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states, reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and the special case for wave is studied briefly.

scholarly journals ROTATIONAL AND VIBRATIONAL DIATOMIC MOLECULE IN THE KLEIN–GORDON EQUATION WITH HYPERBOLIC SCALAR AND VECTOR POTENTIALS

2009 ◽  
Vol 20 (10) ◽  
pp. 1563-1582 ◽  
Author(s):  
SAMEER M. IKHDAIR
Keyword(s):  
Gordon Equation ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Bound State ◽  
Approximate Analytic Solution ◽  
S Wave ◽  
Vector Potentials ◽  
Special Cases ◽  
Klein Gordon ◽  
Klein Gordon Equation

We present an approximate analytic solution of the Klein–Gordon equation in the presence of equal scalar and vector generalized deformed hyperbolic potential functions by means of parametric generalization of the Nikiforov–Uvarov method. We obtain the approximate bound-state rotational–vibrational (ro–vibrational) energy levels and the corresponding normalized wave functions expressed in terms of the Jacobi polynomial [Formula: see text], where μ > -1, ν > -1, and x ∈ [-1, +1] for a spin-zero particle in a closed form. Special cases are studied including the nonrelativistic solutions obtained by appropriate choice of parameters and also the s-wave solutions.

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