Atomic units(au) are a convenient
system of units of measurement used in
atomic physics, particulary 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_0</math>
- charge: the elementary charge <math>e</math>
- energy: the Hartree energy <math>E_h</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>{{{-\hbar^2} \over {2 m_e}}\nabla^2} + {1 \over {4 \pi \epsilon_0}}{{-e^2} \over {r}}</math>
in atomic units:
- <math>{{{-1} \over {2}}\nabla^2} + {{-1} \over {r}}</math>
