The Meaning of |ψ|² in Copenhagen, Bohmian, and Scretching–Planck Mechanics

This paper compares Copenhagen, Bohmian, and Scretching–Planck (SP) accounts of |ψ|² through a detailed analysis of hydrogen. Using the reduced-mass Coulomb model, it derives orbitals, radial probabilities, currents, energy levels, virial relations, contact densities, and transition properties. Calculations yield a ground-state energy of −13.598287264 eV and a first excitation energy of 10.198715448 eV within the ideal model. The analysis explains the conditional SP contact-density energy relation, distinguishes model results from measured values, and demonstrates why local density alone cannot generally determine energy. These results support SP as a density–phase representation of established dynamics without establishing a separate measurement ontology or new predictive extension.