Compton wavelength

The Compton wavelength λ of a particle X is given by λ_X = h / m_Xc, where h is the Planck constant, m_X is the particle's mass and c is the speed of light. A particle generally behaves as quantum mechanically when observed at distances shorter than its Compton wavelength. In particular, in the uncertainty relation for position and momentum, , when the position uncertainty Δx is less than the Compton wavelength, the momentum uncertainty Δp is greater than m_Xc. Since momentum carries energy, the uncertainty in energy is greater than m_Xc², which is enough energy to create another particle of type X. The Compton wavelength is therefore generally viewed as the cutoff below which quantum field theory, which can describe particle creation and annihilation, becomes important.

The Compton length for one Planck mass is equal to the Planck length and is also equal to the Schwarzschild radius of one Planck mass. This is a simple case of dimensional analysis.

Sources

• The Planck Length -- http://math.ucr.edu/home/baez/planck/node2.html
• http://www.physlink.com/Education/AskExperts/ae635.cfm