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Deng-Fan potential for relativistic spinless particles - an ansatz solution. (English) Zbl 1247.81116

Summary: Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schrödinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.

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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