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The scattering of the Manning-Rosen potential with centrifugal term. (English) Zbl 1220.81099

Summary: In this Letter the approximately analytical scattering state solutions of the \(l\)-wave Schrödinger equation for the Manning-Rosen potential are carried out by a proper approximation to the centrifugal term. The normalized radial wave functions of \(l\)-wave scattering states are presented and the calculation formula of phase shifts is derived. It is well shown that the poles of the S-matrix in the complex energy plane correspond to bound states for real poles and scattering states for complex poles in the lower half of the energy plane. We consider and verify two special cases: the \(l=0\) and the \(s\)-wave Hulthén potential.

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
81U05 \(2\)-body potential quantum scattering theory
81U20 \(S\)-matrix theory, etc. in quantum theory
35B34 Resonance in context of PDEs
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