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Arbitrary l-wave scattering state solutions of the Schrödinger equation for the Eckart potential

The approximately analytical scattering state solutions of the l-wave Schrödinger equation for the Eckart potential are carried out by a proper approximation to the centrifugal term. The normalized radial wavefunctions of l-wave scattering states on the ‘k/2π scale’ are presented and the calculation formula of phase shifts is derived. It is interesting to find that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.