Dirac Equation — Zitterbewegung

Trembling motion of free relativistic electron • Interference of positive/negative energy states

Mass m (in ℏ/c units)1.0

Initial momentum p₀0.50

Packet width σ3.0

Sim speed1.0

⟨x⟩ position—

ZB frequency ω_ZB—

ZB amplitude—

Group velocity v_g—

ZB: ⟨x⟩(t) = v_g·t + (ℏ/(2mc))·sin(2mc²t/ℏ)·(positive/neg. energy interference) | ω_ZB = 2mc²/ℏ

Zitterbewegung ("trembling motion") is a rapid oscillation predicted by the Dirac equation for free electrons, arising from interference between positive and negative energy components of the wavepacket. Frequency ω = 2mc²/ℏ ≈ 1.55×10²¹ Hz — too fast to observe directly, but analog systems (trapped ions, graphene) simulate it.