A Krylov-subspace Chebyshev method and its application to pulsed laser-molecule interaction

We present a Krylov-subspace Chebyshev (KSC) method which is especially tailored for computing transition amplitudes. The Hamiltonian matrix is first tridiagonalized using the Lanczos recursive algorithm. The Chebyshev propagator is then used for this tridiagonal matrix to propagate the wave function in the M-dimensional Krylov subspace with high accuracy but negligible cost as compared to the Lanczos step. The dynamics can be extracted from the wave function in the M-dimensional subspace. The method is also extended to the study of molecular interaction with laser pulses and calculations are presented for an illustrative example.