Quantum Mechanical Model of the Hydrogen Atom

Hermann Haken, Hans Christoph Wolf

Bratianu Daniel

This paper tries to prove that the existence and properties of the electron’s spin can be established not only as a consequence of relativistic quantum mechanics, but also as a consequence of non-relativistic quantum mechanics of the Hydrogen atom or Hydrogenic atoms. It is, in fact, an extended model of the Hydrogen atom or Hydrogenic atoms. This new model starts from the assumption that to the foundation of atomic structure there is not only a potential of electrical nature, but also a potential of magnetic nature, which, together with the Coulomb potential, determine the movement of electrons around the atomic nucleus. As a consequence of this new model is obtained a non-relativistic theory of Hydrogen atom which takes into account the spin of the electron and leads us to a non-relativistic theory of the atom in agreement with the Stern-Gerlach experiment results. As well the model can be used in order to explain the spectrum of Alkali-atoms.

Norman Graves

A model is proposed for the hydrogen atom in which the orbiting electron is seen as an objectively real particle. The model is based on the postulate that certain velocity terms can be treated as being affected by relativity. The model provides a mechanism which drives the quantization process and so leads to the discrete energy levels of the atom. The Rydberg formula, being empirically derived, represents the yardstick by which any model for the hydrogen atom must be judged. Rather than develop a model and test it against the Rydberg formula, the approach taken here is to use the Rydberg formula itself as the basis for such a model. The model effectively unifies quantum mechanics with classical mechanics as well as providing a simple mechanical explanation of the Somerfield Fine Structure Constant.

Hermann Haken, Hans Christoph Wolf

Xiao En Wang

Abstract Only Coulomb force is considered in Bohr model. It is found that electron in ground state hydrogen atom is also affected by Lorentz force of the same magnitude. Under the combined action of Coulomb force and Lorentz force, the radius of hydrogen atom is twice that of Bohr, and the rotation frequency of electron is half that of Bohr. The "half frequency" problem of Bohr's theory is solved, and the quantization result of the energy level of hydrogen atom is obtained by using the standing wave condition of quantum mechanics. The mechanism and details of photon absorption by hydrogen atom are analyzed and explained, and the physical meaning of Planck constant is explained.

Hermann Haken, Hans Christoph Wolf