*Volume 2, Issue 1, pages 1-26*

Thomas Allmendinger [Show Biography]

The here presented hydrogen atom model, exemplarily described for its first excited state, proceeds from a previously published model approach by the author [30], applying Newtonian mechanics, too, and hence querying classic quantum mechanics. Thereby the basic concept was maintained, even if considerable corrections were made leading to a significantly different shape of the electron trajectory envelope, namely a spherical one instead of a hyperboloid one. This concept traces back to Bohr’s model, including de Broglie’s standing wave concept, but implies – in contrast to his planar approach – three-dimensional electron trajectories in the (meta-stable) excited states, whereas the electron orbit in the (stable) ground state is planar. The electron trajectories in the excited states can be exactly described by means of a rotating coordinate system, providing three different kinds of velocities (and thus kinetic energies). Thereby the electron behaves like a rotating oscillator. However, this oscillation occurs not linearly, as in the case of a spring pendulum, but curvedly. So the entire motion process is determined by three partial motion processes: a horizontal rotation, a vertical oscillation, and a horizontal deviation which steers the oscillation course. The context to Bohr’s statement that the total angular momentum of the electron is given by the n-multiple of h/2π is insofar difficult to understand as the total angular momentum is split into two parts: an obvious one in the form of the rotation, and a hidden one in the form of the oscillation. A further difficulty arises from the invariability of the angular momentum h/2π. That was not explainable when Bohr proposed his model, neither when de Broglie postulated his wave concept. But it can be explained by the thereafter discovered existence of the electron spin which induces a constant angular momentum, known as the spin/orbit-coupling.

Applying this quantum condition on the electron rotation, and using the normal physical laws concerning the electrostatic Coulomb attraction as well as the centrifugal force, the key values for the respective parameters could be determined at the top position of the electron as well as at its position at the equator. Surprisingly the distance between the proton (nucleus) and the electron remains constant. In a next step, the oscillation frequency was determined employing these values and applying the usual formula for a harmonic oscillator. It serves as a time base for any temporally variable processes. Derived from this, the motion regularity of the deviation process could be determined. Finally, the time dependency of the rotation angle could be determined by taking into account de Broglie’s standing wave condition.

This oscillating process is insofar peculiar as it is not achieved by a transmutation of potential energy into kinetic energy and vice versa, as it is the case at a spring pendulum, but by a transmutation of different kinds of kinetic energies at a constant potential energy. Due to this, the electron can move on a spherical segment at a constant distance which is identically equal to the respective Bohr radius. Thereby, the motion occurs along a three-dimensional wavy spiral line, whereas in Bohr’s model it solely describes a simple planar circle. But in particular, a stringent correlation of this oscillation frequency ν0 and the total energy of the electron could be revealed, analogously to Einstein’s formula for the photoelectric effect, namely Etot = h · ν0. Thus it proves the equity of the electron frequency and the light frequency at the absorption/emission process.