Abstract
A new approach is presented for the computation of quantum mechanical time-dependent transition probabilities in systems with a large number of states. Following use of the Lanczos algorithm to produce a tridiagonal representation (J) of the perturbed Hamiltonian, a modification of the QL algorithm is introduced to compute eigenvalues and the first row (only) of the eigenvector matrix of J . All of the eigenvalues and eigenvector coefficients are used to compute transition amplitudes, even though roundoff error during Lanczos recursion causes spurious eigenvalues to appear. This contrasts with the original version of the recursive residue generation method (RRGM), where a condensed eigenvalue list was produced (via the CullumWilloughby procedure) before computing squares of eigenvector coefficients. Eigenvalues, residues, and time dependent transition probabilities computed from the two methods are found to be equivalent.
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