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.

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.

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

2009 ◽  
Vol 24 (17) ◽  
pp. 1371-1382 ◽  
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.

Scattering State of Coupled Hulthen–Woods–Saxon Potentials for the Duffin–Kemmer–Petiau Equation with Pekeris Approximation for the Centrifugal Term

2015 ◽  
Vol 70 (3) ◽  
pp. 185-191 ◽  
Author(s):  
Akpan N. Ikot ◽  
Hillary P. Obong ◽  
Joy D. Olisa ◽  
Hassan Hassanabadi
Keyword(s):  
Energy Spectrum ◽  
Wave Functions ◽  
Centrifugal Term ◽  
Saxon Potential ◽  
Radial Wave ◽  
Dkp Equation ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Pekeris Approximation

AbstractWe studied the approximate analytical scattering state of the Duffin–Kemmer–Petiau (DKP) equation for arbitrary l-state for couple Hulthen–Woods–Saxon potential using the Pekeris approximation for the centrifugal term. We obtained an energy spectrum, normalised radial wave functions of the scattering states, and the corresponding formula for the phase shifts, which is derived in detail. Special cases of Hulthen and Woods–Saxon potentials were also studied.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals BOUND STATES OF THE KLEIN–GORDON EQUATION IN THE PRESENCE OF SHORT RANGE POTENTIALS

2006 ◽  
Vol 21 (02) ◽  
pp. 313-325 ◽  
Author(s):  
VÍCTOR M. VILLALBA ◽  
CLARA ROJAS
Keyword(s):  
Short Range ◽  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

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