Atomic unit of length - Definition

Atomic units(au) are a convenient system of units of measurement used in atomic physics, particularly for describing the properties of electrons. The atomic units have been chosen such that the fundamental electron properties are all equal to one atomic unit.

The atomic units are:

length: the Bohr radius <math>a_0<math>

mass: the electron rest mass <math>m_e<math>

charge: the elementary charge <math>e<math>

energy: the Hartree energy <math>E_h<math>

angular momentum: the Dirac constant <math>\hbar <math>

The use of atomic units also simplifies the Schrödinger equation. For example the Hamiltonian for an electron in the hydrogen atom would be:

in SI units:

<math>\hat H ={{{-\hbar^2} \over {2 m_e}}\nabla^2} + {1 \over {4 \pi \epsilon_0}}{{-e^2} \over {r}}<math>

in atomic units:

<math>\hat H ={{{-1} \over {2}}\nabla^2} + {{-1} \over {r}}<math>