Multiple States in the Hydrogen Atom.

Cynthia Kolb Whitney

The hydrogen atom is the gateway atom for the development of the quantum mechanics of all atoms, and hence all molecules, and hence all nanostructures. A more conservative analysis of the hydrogen atom just identifies the approximations that caused the classical analysis to go badly, and removes those approximations. The basic approach to the hydrogen atom that can be characterized as follows: take account of all processes that can be identified, and look for a natural balance between them. There exist other research areas awaiting further application of this approach. Hydrogen atoms, and all other atoms as well, are presently envisioned as having infinitely many ‘excited states’ that are described via the multiple solutions of Schrodinger’s differential equation for the atom. These excited states are presently understood as conditions that an individual atom possesses. The ionization potential of helium is very high–the highest among all elements. It invites the interpretation that electrons very much like to form a pair.

Randell L Mills

Koshun Suto

The phase velocity of a material wave is given by the following equation: If this formula is rewritten using the Planck-Einstein relation and the de Broglie formula , it becomes: Next, the values for E and p, obtained from a relation applicable to the electron in a hydrogen atom derived by the author, are substituted into this equation. When that is done, multiple formulas relating to the phase velocity of the electron wave are derived. These formulas contain still-unknown ultra-low energy levels of the hydrogen atom and electron orbital radii corresponding to those energy levels. also appear in the formula for energy levels of the hydrogen atom derived in this paper. This serves as grounds for the existence of ultra-low energy levels in addition to the already-known energy levels of the hydrogen atom.

John C. Morrison

Eite Tiesinga, Henk T. C. Stoof, BOUDEWIJN J. VERHAAR

We propose a new method for studying the reflection of a hydrogen atom from a superfluid-helium film. Starting from the narrow width of the reflected angular distribution recently found experimentally, we tentatively extrapolate to the extreme limit of low ripplon wave numbers in which the adiabatic or degenerate-internal-states approximation becomes valid. We obtain simple closed expressions for single- and multiple-ripplon processes, which do not require the integration of a Schr\"odinger equation for their evaluation and do not depend on the specific form of the potential.

Peter Bongaarts