Molecular Dipole Function Inversion from Time Dependent Probability Density and Electric Field Data

Abstract

A noniterative quantum mechanical algorithm is presented to extract the dipole function from time dependent probability density and external electric field data. The algorithm determines the dipole function as the solution of an exact linear integral equation without the need to solve the Schrodinger equation. The inversion in regular regions of the dipole is accurate and stable under perturbations from noisy data. The regular regions of the dipole are automatically identified by the algorithm, and Tikhonov regularization is employed. There is much freedom in the external electric field with the best choices generally producing broad excitations of many eigenstates. Field designs may be estimated from the Hamiltonian or through closed loop learning techniques in the laboratory. The inversion algorithm is tested in a simulation for O−H, which shows that the algorithm is very reliable. Since the inversion algorithm is fast, it is argued that closed loop laboratory learning techniques may be applied to optim...