Wavelet solution of the time independent Schrödinger equation for a rectangular potential barrier

Electronics industry is a major user of Metal-Insulator-Metal (MIM) structures. When the tunneling phenomenon occurs at the metal-insulator contact barrier, as for the MIM structures, we are dealing with the Fowler-Nordheim field emission. In MIM structures we have to calculate the currents densities that go through. Unfortunately, the calculation methods currently used lead to values that get predictions of emission current density too low. The current density is calculated based on the transmission coefficient through the barrier, which is determined by solving the Schrödinger equation. One of the oldest and most efficient methods of solving the Schrödinger equation is the WKB method. This paper proposes the wavelet method for solving the 1D Schrödinger equation, that is: determining the wave function using the harmonic multiresolution analysis.