Simulation of a hydrogen atom in a laser field using the time-dependent variational principle

The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrodinger equation in one and three dimensions for a one-body soft Coulomb potential in a laser field. The accuracy is tested comparing the solution to finite difference grid calculations using several examples. The approach is not limited to one particle systems and the example presented for two electrons demonstrates the potential to tackle larger systems using correlated basis functions.