Wronskian analysis of resonance tunnelling reactions

A Wronskian formalism is developed for resonance tunnelling reactions. It is shown how the S matrix can be written in terms of Wronskians between solutions of the Schrödinger equation representing incoming and outgoing waves. The method is an adaptation of the Jost function approach to elastic two-body scattering. Formal expressions are derived for the imaginary parts of the energy eigenvalues that arise from the application of complex boundary conditions used in a previous semiclassical analysis. When the imaginary parts are small, so that the resonance is sharp, the S matrix can be written in a Breit-Wigner resonance form. The theory unifies and extends the semiclassical analysis of resonance tunnelling reactions given previously.