Hartree atomic units
Name Symbol/Definition Value in atomic units
speed of light c { \displaystyle c } ( 1 / α ) a 0 E h / ℏ ≈ 137 a 0 E h / ℏ { \displaystyle ( 1/\alpha ) \ , a_ { 0 } E_ { \text { h } } /\hbar \approx 137\ , a_ { 0 } E_ { \text { h } } /\hbar }
classical electron radius r e = 1 4 π ϵ 0 e 2 m e c 2 { \displaystyle r_ { \mathrm { e } } = { \frac { 1 } { 4\pi \epsilon _ { 0 } } } { \frac { e^ { 2 } } { m_ { \mathrm { e } } c^ { 2 } } } } α 2 a 0 ≈ 0.0000532 a 0 { \displaystyle \alpha ^ { 2 } \ , a_ { 0 } \approx 0.0000532\ , a_ { 0 } }
reduced Compton wavelength of the electron ƛ e = ℏ m e c { \displaystyle = { \frac { \hbar } { m_ { \text { e } } c } } } α a 0 ≈ 0.007297 a 0 { \displaystyle \alpha \ , a_ { 0 } \approx 0.007297\ , a_ { 0 } }
Bohr radius a 0 = ℏ m e c { \displaystyle a_ { 0 } = { \frac { \hbar } { m_ { \text { e } } c } } } 1 a 0 { \displaystyle 1\ , a_ { 0 } }
proton mass m p { \displaystyle m_ { \mathrm { p } } } m p ≈ 1836 m e { \displaystyle m_ { \mathrm { p } } \approx 1836\ , m_ { \text { e } } }
Physical constants
The Hartree atomic units are a system of natural units of measurement which is especially convenient for atomic physics calculations. They are named after the physicist Douglas Hartree. In this system the numerical values of the following four fundamental physical constants are all unity by definition:
In Hartree atomic units, the speed of light is approximately 137 atomic units of velocity. Atomic units are often abbreviated a.u. or au, not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in other contexts.