Аннотация:Usually, when theoretical studying the spectra of high harmonic generation by an atomic system, a semiclassical approach is applied, based on the Fourier transform of the dipole moment induced by an intense laser pulse and averaged over the solution of the time-dependent Schrödinger equation (TDSE). From fist principles, the results should not depend on the unitary transformation of the exact solution of the TDSE. In reality, there is a violation due to approximations, especially for multielectron atoms. The degree of the difference may be a sign of the accuracy of the method used.We consider two expressions (in atomic units) for the laser-atom interaction operator in the TDSE V ̂(t)=D∙F(t) (length gauge) and V ̂'(t)=c^(-1) P ̂∙A(t)+A^2 (t)/(2c^2) (velocity gauge), where D is the atomic dipole moment operator, P ̂ is the total electron momentum operator, F(t) and A(t) are the classical field strength and the vector potential of the laser field, respectively, coupled by the relation F(t)=-c^(-1) ∂A/∂t. The corresponding solutions of the TDSE are related by the unitary transformation 〖Ψ^' (t)=exp〗〖[-iD∙A(t)/c]Ψ(t)〗.In our study, we expand the TDSE solution of the Ga+ ion in a femtosecond laser field over a finite superposition of discrete stationary states of an unperturbed target obtained in the Hartree-Fock model [1]. By comparing the results obtained in both gauges, we control the expansion basis with respect to its completeness and the approximation of the basis states.The work was supported by the Russian Science Foundation (project No. 22-12-00389}.