The relativistic problem of spin-1/2 particles subject to the Woods-Saxon potential is investigated by using the functional analysis method. We obtain scattering and bound state solutions of the one-dimensional Dirac equation with the Woods-Saxon potential in terms of the Jacobi polynomials. We also calculated the transmission and reflection coefficients by using behavior of the wave functions at infinity.
In this letter, the scattering state solutions of the Dirac equation for spin and pseudospin symmetries are obtained for the Hellmann potential. The normalized wave functions and scattering phase shifts are calculated for both spin and pseudospin symmetries. Scattering properties for Coulomb-like and Yukawa-like potentials are also studied as limiting cases.
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