  A combination of the variable-constant and complex coordinate rotation
methods is used to solve the two-body Schr\"odinger equation. The latter is
replaced by a system of linear first-order differential equations, which
enables one to perform direct calculation of the Jost function for all complex
momenta of physical interest, including the spectral points corresponding to
bound and resonance states. Explicit forms of the equations, appropriate for
central, noncentral, and Coulomb-tailed potentials are given. Within the
proposed method, the scattering, bound, virtual, and resonance state problems
can be treated in a unified way. The effectiveness of the method is
demonstrated by a numerical example.
