Analytical solutions of the Klein-Gordon equation with a combined potential. (English) Zbl 1539.81056
Summary: The supersymmetric approach is employed to calculate any \(\ell\)-state solutions of the Klein-Gordon equation in the non-relativistic limit of potential \(V\) with a combined potential by using a proper approximation scheme to the centrifugal term. The energy equation and the corresponding unnormalized wave function are obtained analytically. The non-relativistic limit is obtained and numerical results are computed for some values of \(n\) and \(\ell\) with \(\sigma = 0.1\), 0.2, 0.3 and 0.4 using MATLAB 7.5.0.342 programing. In a more interesting form, we studied some special cases and compared our results with the previous once.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81Q60 | Supersymmetry and quantum mechanics |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
Software:
MatlabReferences:
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