The Shubnikov - de Haas and the de Haas - van Alphen effects in bulk crystals and low-dimension structures

The Shubnikov and de Haas (SdH) as well as de Haas and van Alphen (dHvA) effects that allow the identification of quantum-dimensional processes of the energy and magnetic moment in solids are analyzed within frameworks of the classical Landau level formation under the conditions of the prolonged movement of carriers in three- and two-dimensional systems. The methods that are based on the SdH and dHvA effects are possible to be used as the powerful instrument to study quantum interference processes for the studies of the semiconductor nanostructures, with the dimensions close to the Fermi wavelength.