Bohmian Mechanics, Copenhagen, and the Scretching Planck Interpretation

This paper compares Bohmian mechanics, Copenhagen interpretations, and the Scretching–Planck (SP) density–phase formulation, emphasizing the relationship between quantum density and energy. An exact contact-density relation for nonrelativistic Coulomb nS states reproduces Bohr’s hydrogen energies and photon transition energies under matching assumptions, including the approximately 10.1987154 eV transition from n = 1 to n = 2. Extensions to many-electron atoms, molecules, and free electrons clarify the limits of density as an energy proxy and the role of phase in kinetic energy. Electromagnetic coupling, selection rules, and measurement assumptions remain essential. No universal density-only energy law or new experimental validation is claimed.