The Schrödinger Equation

Abstract

The finest scale in the matter description consists of the one of quantum mechanics. In this chapter we revisit some valuable concepts of quantum mechanics, and more particularly the Schrödinger equation governing the time evolution of the so-called wavefunction, from which expectations can be easily derived. Another important output is the interatomic potentials responsible of the chemical bonds determining the structure and properties of materials. Even if the quantum framework is able to define the big picture, an important difficulty remains: the Schrödinger equation is defined in a highly multidimensional space and its solution is in most cases unattainable.