Quantum Physics

**Reduced mass** *μ*

Reduced mass *μ* is used throughout physics and engineering as a correction ‘factor’ for interacting particles whose interaction affects the centre of mass. It is given by

where *m* is the mass of the particle and *M* is the mass of the particle it interacts with. For example, the
reduced mass *μ _{e}* of an orbital electron is given by

where *m _{e}* is the mass of the orbiting electron and

*m*is the mass of the proton. This is due to their mutual interaction given by Newton’s Third Law of Motion, which causes the two to rotate about a mutual origin of orbit, instead of at the centre of mass of either one of the particles.

_{p}# Multiple bodies

The reduced mass *m _{N}* of

*N*mutually interacting bodies is given by

where *m _{n}* is the mass of the

*n*th body.

# Relativistic correction

*See posts about special relativity*.

The reduced mass often sees an additional relativistic
correction, given for *N* bodies by

since *m*_{rel} = *γm* for a rest mass *m*. Note that *γ _{n}* is the Lorentz factor for the

*n*th body travelling at velocity

*v*≈

_{n}*c*, defined such that

For only **two bodies**, this simply becomes