The explicit Lanczos wave packet propagation

This chapter deals with the explicit Lanczos wave packet propagation. To get the spectrum of evolution operator U^(τ) diagonalization techniques could be used with the Schrödinger basis set {| φn)}. Such a basis is delocalized, causing matrices to be full, and this enhances the ill-conditioning of the problem. One way to obtain sparse diagonalizing matrices is provided by switching from {| φ_n)} to the Lanczos basis set {| ψ_n)} where the vectors {| ψ_n)} are implicitly generated via recursion. The resulting evolution matrix U(τ) is tridiagonal.