ABSTRACT
The Schrodinger equation is the main equation of non-relativistic quantum mechanics. In quantum mechanics, each physical quantity corresponds to its own operator; so this equation is written with operators. The time-dependent Schrodinger equation describes the behaviour of a non-relativistic particle governed by the laws of quantum mechanics. The electronic environment is dimensionally reduced from a 2-D quantum well to a 1-D quantum wire and to a 0-D quantum dot, where dimensionality is related (in this context) to the number of freedom degrees of the electron moment. The energy levels Ei of the system can be deduced from the results of quantum mechanics, using the Schrödinger equation. The most general approaches describe dmechanical particles, nuclei and electrons, governed by the Schrodinger equation. The 3-D simulations of nanoelements involve a self-consistent solution of a 3-D Poisson equation and a 3-D Schrödinger equation with open boundary conditions.
