On Schrödinger's Equations – part 1

DE BROGLIE's conception of phase harmony has been applied to the scalar wave equation, for which the always supra-luminal propagation speed is determined by the primordial condition of least action, from which the relativistic form of SCHRÖDINGER's equations naturally follows. In this form, a new but not unexpected parameter appears, the Lorentz factor. The time-independent orbital energy equation derived for charged massive particles (equation 20) is interpreted as directly describing an equipartition theorem for which the total kinetic energy of relative motion is equal parts translation (orbital) and internal rotation (spin). This equation also describes the impossibility of a sustained thermodynamic state of absolute zero temperature. In this framework, normalization of bound-state wave functions is interpreted as an accounting of the energy density in the electromagnetic fields that bind charged massive particles together to form stable composite systems. Solutions to the reduced-mass 1/r^2 central-force problem for two body and symmetric three body systems can now be perceived as describing a planetary-like model of spinning charged massive particles of definite size executing perfectly circular orbits about a stationary center of mass. The time-dependent resonance problem of collision-induced photon absorption and emission and its solution are reviewed, further indicating that quantum mechanics and theories of relativity are united through wave equations; SCHRÖDINGER'S misapplication of DE BROGLIE's phase harmony theorem disunited these two pieces at the outset.