  The Jost function formalism is extended with use of the complex potential in
this paper. We derive the Jost function by taking into account the dual state
which is defined by the complex conjugate the complex Hamiltonian. By using the
unitarity of the S-matrix which is defined by the Jost function, the optical
theorem with the complex potential is also derived. The role of the imaginary
part of the complex potential for both the bound states and the scattering
states is figured out. The numerical calculation is performed by using the
complex Woods-Saxon potential, and some numerical results are demonstrated to
confirmed the properties of extended Jost function formalism.
