Scattering states solutions of Klein–Gordon equation with three physically solvable potential models

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.

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

Physics Letters A ◽

10.1016/j.physleta.2004.08.017 ◽

2004 ◽

Vol 330 (6) ◽

pp. 424-428 ◽

Cited By ~ 32

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

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

Open Physics ◽

10.2478/s11534-008-0143-9 ◽

2009 ◽

Vol 7 (1) ◽

Cited By ~ 27

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.

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THE APPROXIMATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION WITH THE SECOND PÖSCHL–TELLER LIKE POTENTIAL FOR NONZERO ANGULAR MOMENTUM

Modern Physics Letters A ◽

10.1142/s0217732309028825 ◽

2009 ◽

Vol 24 (17) ◽

pp. 1371-1382 ◽

Cited By ~ 1

Author(s):

WEN-LI CHEN ◽

GAO-FENG WEI ◽

WEN-CHAO QIANG

Keyword(s):

Bound States ◽

Gordon Equation ◽

S Wave ◽

Radial Wave ◽

Scattering States ◽

Approximate Analytical Solutions ◽

Scattering State ◽

Klein Gordon ◽

Energy Plane ◽

Klein Gordon Equation

The approximate analytical bound and scattering state solutions of the arbitrary l-wave Klein–Gordon equation for the second Pöschl–Teller like potential are carried out by a new approximation to the centrifugal term. The analytical radial wave functions of the l-wave Klein–Gordon equation with the second Pöschl–Teller like potential are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is well shown that the poles of S-matrix in the complex energy plane correspond to bound states for real poles and scattering states for complex poles in the lower half of the energy plane. Some numerical results are calculated to show the improved accuracy of our results and the special case for s-wave is also studied briefly.

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Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

Open Physics ◽

10.2478/s11534-008-0099-9 ◽

2008 ◽

Vol 6 (4) ◽

Cited By ~ 2

Author(s):

Chang-Yuan Chen ◽

Fa-Lin Lu ◽

Dong-Sheng Sun

Keyword(s):

Analytical Solutions ◽

Hypergeometric Functions ◽

Gordon Equation ◽

Approximate Analytical Solution ◽

Wave Functions ◽

Calculation Formula ◽

Scattering States ◽

Approximate Analytical Solutions ◽

Klein Gordon ◽

Klein Gordon Equation

AbstractIn this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.

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