Semiclassical Analysis of the Schrödinger equation with a partially confining potential

International audienceThe semiclassical limit of a partially confined electron gas is performed. The length scale in the confined direction is of the order of magnitude of the electron de Broglie length whereas the non confined lengthscale is larger. A partial semiclassical limit of the Schrödinger equation (in the non confined direction) is performed and leads to the so-called subband model. The limiting behaviour is described by an infinite number of quasistatic Schrödinger equations for the confined direction and an infinite number of time-dependent Vlasov equations in the non confined direction