Analytical evaluation of the energy derivative of the S matrix in the time-independent wavepacket approach to quantum scattering

Abstract

We consider the evaluation of energy derivatives of the S matrix, d S( E)/d E, using our recently developed time-independent wavepacket (TIW) theory of quantum scattering. This approach, combined with a polynomial representation of the full time-independent Green function, results in analytical expressions for the energy dependence of S( E), and d S( E)/d E)/d E. Specific expressions are based on Chebychev polynomials, but the approach is general, for any choice of orthogonal polynomials. Analytical expressions for S( E) and d S( E)/d E make possible simultaneous evaluation of the lifetime or time-delay matrix and the S-matrix for any energies desired.