# Atomic units

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:

mass: the electron rest mass [itex]m_e[itex]
charge: the elementary charge [itex]e[itex]
angular momentum: the Dirac constant [itex]\hbar[itex]
energy: the Hartree energy [itex]E_h[itex]

The electrostatic force constant [itex]k = 1/4\pi \epsilon_0[itex] is also equal to one in this system. In fact, these six quantities are not all independent; it is sufficient to define any four of these constants to be one.

In atomic units, the Bohr magneton [itex]\mu_B = 1/2[itex], and the speed of light [itex]c = 1/\alpha \approx 137.036[itex], where [itex]\alpha[itex] is the fine-structure constant.

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:

[itex]\hat H = - {{{\hbar^2} \over {2 m_e}}\nabla^2} - {1 \over {4 \pi \epsilon_0}}{{e^2} \over {r}}[itex]

in atomic units:

[itex]\hat H = - {{{1} \over {2}}\nabla^2} - {{1} \over {r}}[itex]

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