nLab
Compton wavelength

Context

Physics

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Contents

Definition

The Compton wavelength is a physical unit that governs the dispersion relation/energy-momentum relation of massive fields.

For a particle/field of mass mm, its Compton wavelength is the length

m2πmc \ell_m \coloneqq \frac{2\pi \hbar}{m c}

where cc denotes the speed of light and 2π2\pi\hbar denotes Planck's constant. Correspondingly mc\frac{\hbar}{m c} is also called the “reduced Compton wavelength”.

The inverse of the Compton wavelength appears as the mass term notably in the Klein-Gordon equation of the scalar field or the Dirac equation of the Dirac field.

Examples

  • The Compton wavelength corresponding to the mass of the electron is about m e~386\ell_{m_e} ~ 386 fm.

  • Another length scale parameterized by a mass mm is the Schwarzschild radius r m2mG/c 2r_m \coloneqq 2 m G/c^2, where GG is the gravitational constant. Solving the equation

    m = r m 2π/mc = 2mG/c 2 \array{ & \ell_m &=& r_m \\ \Leftrightarrow & 2\pi\hbar / m c &=& 2 m G / c^2 }

    for mm yields the Planck mass

    m P1πm =r=cG. m_{P} \coloneqq \tfrac{1}{\sqrt{\pi}} m_{\ell = r} = \sqrt{\frac{\hbar c}{G}} \,.

    The corresponding Compton wavelength m P\ell_{m_{P}} is given by the Planck length P\ell_P

    P12π m P=Gc 3 \ell_{P} \coloneqq \tfrac{1}{2\pi} \ell_{m_P} = \sqrt{ \frac{\hbar G}{c^3} } \,

References

Last revised on November 9, 2017 at 05:12:46. See the history of this page for a list of all contributions to it.