Excitation and ionization of a particle in a one-dimensional potential well of zero radius by an extremely short light pulse

The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric area of the pulse to the characteristic “scale” of the area inversely proportional to the size of localization of the particle in a bound state.