Exact RQM

Closed-form solutions of the Klein–Gordon and Dirac equations, each one checked against the equation as you watch, and 2D wave packets that show the Schrödinger equation as their v ≪ c limit.

Equation
Solution

Simulation units: ℏ = c = mo = 1, so lengths are in reduced Compton wavelengths ℏ/moc, times in ℏ/moc², energies in moc², and qA is absorbed into the potential. Formulas are written in SI with c and ℏ explicit. Metric signature (+,−,−,−); (∂·∂) = ∂²/c²∂t² − ∇². Dirac matrices in the Dirac representation. Nothing on this page is looked up: every plot is computed from the closed-form wavefunction, and the Verify tab substitutes it back into its equation.