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A new computational approach to time-dependent transition amplitudes in multistate quantum systems is developed. The method, which avoids explicit computation of matrix eigenvectors, is based upon the recursive generation of residues of Green's functions. The residues are computed from the eigenvalues of several tridiagonal matrices. Numerical results are presented for multiphoton excitation of overtones in a system with over 3000 states.
Nauts et al. (Mon,) studied this question.