Pekeris approximation – another perspective. (English) Zbl 1295.81053
Summary: Inspired on the Pekeris approximation for the centrifugal term, we elaborate a method of resolution for the Schrödinger equation subject to a potential \(V(r)\) of a form more general than the exponential one. Generalizing the Pekeris approximation, we solve the Schrödinger equation with Rosen-Morse and Manning-Rosen potentials including the centrifugal term. The bound state energy eigenvalues for these potentials and for arbitrary values of \(n\) and \(l\) quantum numbers are presented.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
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