  We study theoretically the quantum dynamics of an electron in the symmetric
four-level double-dot structure under the influence of the monochromatic
resonant pulse. The probability amplitudes of the eigenstates relevant for the
quantum dynamics are found from the solution of the non-stationary
Schr\"odinger equation. The first-order correction term to the solution
obtained through the rotating wave approximation is calculated. The three-level
double-dot dynamics and the two-level single-dot dynamics, as well as the
off-resonant excitation process, are derived from the general formulae for
corresponding choices of the pulse and structure parameters. The results
obtained may be applied to the solid-state qubit design.
