| _version_ | 1866901782248030208 |
|---|---|
| author | Miller, James |
| author_facet | Miller, James |
| contents | <p>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.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19242119 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Planck Relation from Helical Wave Mechanics Miller, James <p>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.</p> |
| title | The Planck Relation from Helical Wave Mechanics |
| url | https://doi.org/10.5281/zenodo.19242119 |