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Published equation contexts

ωZ=2Mc2ℏ\omega_Z = \frac{2Mc^2}{\hbar}

Why this formula appears here

The Newton–Wigner operator was not built for elegance; it was built to repair a specific, observable pathology in the naive Dirac position operator x^\hat{\mathbf x} , the coordinate that appears literally in the Dirac equation. Because a free Dirac wavepacket generically mixes positive- and negative-energy plane-wave components, x^\hat{\mathbf x} 's Heisenberg equation of motion picks up, alongside the ordinary uniform drift, an oscillating term with no classical counterpart: an angular frequency ωZ=2Mc2ℏ\omega_Z = \frac{2Mc^2}{\hbar}. set purely by the rest mass. For an electron this is ωZ\omega_Z ≈\approx 1.55×\times10^{21}\ rad s−1\mathrm{rad\,s^{-1}} , an oscillation period of roughly four zeptoseconds in the particle’s…

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ωZ\omega_Z

Symbol omega_Z

omegaZa_Z is part of the quantity the equation computes from the expression on the right.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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ωZ=2Mc2ℏ,\omega_Z = \frac{2Mc^2}{\hbar},

Equation 70 · Evolutionary Physics

The Atlas That Refuses to Close

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The Newton–Wigner operator was not built for elegance; it was built to repair a specific, observable pathology in the naive Dirac position operator x^\hat{\mathbf x} , the coordinate that appears literally in the Dirac equation. Because a free Dirac wavepacket generically mixes positive- and negative-energy plane-wave components, x^\hat{\mathbf x} 's Heisenberg equation of motion picks up, alongside the ordinary uniform drift, an oscillating term with no classical counterpart: an angular frequency ωZ=2Mc2ℏ\omega_Z = \frac{2Mc^2}{\hbar}. set purely by the rest mass. For an electron this is ωZ\omega_Z ≈\approx 1.55×\times10^{21}\ rad s−1\mathrm{rad\,s^{-1}} , an oscillation period of roughly four zeptoseconds in the particle’s…

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