Application of parabolic wave packets to solving the evolution problem of a hydrogen atom exposed to long laser pulses

The article studies the features of application of the parabolic wave packets (PWP) (we proposed) to the solution of the Time-Dependent Schrödinger Equation (TDSE) for a hydrogen atom exposed to a long laser pulse. Within the framework of the Time-Dependent Variational Principle, the TDSE is transformed into a system of first-order differential equations with respect to the PWP parameters. The efficiency of the proposed scheme has been studied using an exactly solvable example of pulses of arbitrary (including complex) amplitude and duration. The case of ultraviolet radiation was also considered, for which our calculations were compared with the results obtained by other authors. Possible reasons for the observed discrepancy between the results of applying our approach and those obtained by standard methods were listed.