For the theory of drift plasma and β-plane geophysical dynamics both large-scale vortex and small-scale wave components are important: linear excitation and dissipation occur mainly at small scales, while concentration of the energy spectrum takes place (through the inverse cascade) at large vortices. Based on the time and space separation of these scales averaged evolution equations are derived. The equation for the small scales describes the propagation of high-frequency quanta on the background of a flow produced by large-scale vortices; this equation provides the conservation of the spectral density of the potential enstrophy of small scales. The equation for the large-scale component is the Charney-Hasegawa-Mima equation with a source term having the form of the ponderomotive force and providing the inverse energy cascade from small to large scales. A new computational approach for the modeling of drift and β-plane turbulence is proposed on the basis of the equations obtained - the quantum in the cell method.