Wave functions

To understand the nature of electrons in atoms and molecules needs the use of quantum mechanics. This theory guesses the allowed quantized energy levels of a system and has other characteristics that are very distinct from 'classical' physics. Electrons are explained by a wave function, which consists of all the information we can know about their behaviour. The standard notion of a definite trajectory (for example the motion of a planet around the Sun) is not valid at a microscopic level.

The quantum theory considers only probability distributions, which are given by square of the wave function and which show where electrons are more or less likely to be found. The Solutions of Schrödinger's wave equation provide the allowed energy levels and the subsequent wave functions. Wave functions for atoms are known as atomic orbitals, by analogy with the orbits of electrons in the classical planetary model. Correct solutions of Schrödinger's equation can be obtained only for one-electron atoms and ions, but atomic orbitals that are the result from these solutions give pictures of the nature of electrons which can be extended to several-electron atoms and molecules.