Relations between the wave solutions and the jost solutions off the energy shell for local central potentials

Using the Green function techniques we express the wave solutions of the radial inhomogeneous Schrödinger equation by means of the on-shell Jost and regular solutions. Making use of their boundary behaviour atr = andr = 0 we reexpress them alternatively in terms of the off-shell Jost and regular solutions. Relations among the different generalized (fully off the energy shell) Jost functions are derived and the radial matrix elements of the transition and reaction (reactance) operators are given in terms of these Jost functions. The relations reflect the principle of detailed balance.