We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zero-reflection condition depends on the shape of the potential.

arXiv:hep-th/0503108Physical Review AMay 9, 200578 citations

Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method

Sameer M. Ikhdair, R. Sever

The exact solution of the one-dimensional Klein-Gordon equation of the 𝒫𝒯-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials.

arXiv:quant-ph/0610183Annalen der PhysikDec 21, 200671 citations