Arbitrary \(l\)-wave solutions of the Schrödinger equation with the Hulthén potential model. (English) Zbl 1175.81095
Summary: By using an improved new approximation scheme to deal with the centrifugal term, we investigate the bound state solutions of the Schrödinger equation with the Hulthén potential for the arbitrary angular momentum number. The bound state energy spectra and the unnormalized radial wave functions have been approximately obtained by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our approximate analytical results are in better agreement with those obtained by using numerical integration approach for small values of the screening parameter \(\delta \) than the other analytical results obtained by using the conventional approximation to the centrifugal term.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
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