Bound-state solutions of the Klein-Gordon equation with \(q\)-deformed equal scalar and vector Eckart potential using a newly improved approximation scheme. (English) Zbl 1362.81027
Summary: We present the analytical solutions of the Klein-Gordon equation for \(q\)-deformed equal vector and scalar Eckart potential for arbitrary \(l\)-state. We obtain the energy spectrum and the corresponding unnormalized wave function expressed in terms of the Jacobi polynomial. We also discussed the special cases of the potential.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81Q60 | Supersymmetry and quantum mechanics |
| 81U15 | Exactly and quasi-solvable systems arising in quantum theory |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81V45 | Atomic physics |
| 81V55 | Molecular physics |
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