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Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

100%
Wei G.-F., Qiang W.-C., Chen W.-L.
Open Physics
|
2010
|
vol. 8
|
issue 4
574-579
EN
The continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.
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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

100%
Wei G.-F., Zhen Z.-Z., Dong S.-H.
Open Physics
|
2009
|
vol. 7
|
issue 1
175-183
EN
The 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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