A quantum model is derived and implemented for the detailed investigation of high-speed and high-frequency quantum devices. For the first time the electron wave-functions and depth profiles are computed for single- and multiple-quantum well MODFETs. The charge distribution in the channel(s) reveals multiple local maxima in agreement with experimental data. The influence of bias conditions and device parameters is studied at room- and liquid nitrogen temperatures. Finally, the limits of classical approaches using Fermi-Dirac statistics, or analytic formulations, are discussed. The latter is found lo be conducive to a reduced spreading of the electron profile in the channel, with direct influence on the value of the gate capacitance.