Wave-function representation by means of a system of nonorthogonal functions and allowance for the contribution of the discrete levels of a single-particle system to the probability of its multiphoton ionization

A representation of a wave function by means of a system of nonorthogonal functions is proposed in order to describe the process of multiphoton transition of a material system from a ground state to the continuous spectrum with allowance for the other discrete levels. Equations are derived for the wave function in this approximation. Application of perturbation theory to these equations makes it possible to obtain a first-approximation description of the system in the discrete part of the spectrum independently of the continuous spectrum. The solution obtained for the discrete levels is used to calculate the probability of a transition of the system of the continuous spectrum. It is possible to describe multiphoton ionization in the first order of perturbation theory.