The Planck Relation from Helical Wave Mechanics

We derive E = hf — the Planck relation — from the geometry of the quantum wave function. The wave function traces a helix (proven via constant curvature and torsion). Combining this with one experimental input (angular momentum quantized as L = ℏ per photon) and the virial theorem, the derivation yields E = ℏω = hf in four lines of algebra. The proportionality constant h is determined exactly by the cancellation of 1/2 from rotational kinetic energy with the factor of 2 from the virial theorem — no fitting, no free parameters. The Planck relation, assumed as a postulate since 1900, is shown to be a derivable consequence of helical geometry and quantized angular momentum.