Atomic Energy Levels

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.

T. S. Subbaraya, Kalkunte S. Seshadri, N. A. Narayana Rao

Pieter Kok

Jiao Zhi-wei

The forbidden band in a photonic crystal leads to the existence of trapped atom-field state whose properties depend on the followings: the number of atoms embedded in a photonic crystal,the energy level structure of atom,the relative position between the level and the edge of band gap and the existence of driving field.By using the method of searching for the eigenstate of the trapped state,that the trapped atom-field state for a three-level atom with driving field in a photonic crystal exists due to the interference between atom and field, was discussed. That the trapped states and the population in various levels can be influenced by the strength and the Rabi frequency of the driving field was proved. That more than one trapped state exist and they depend on the position of the upper level also were proved. Analysis show that there is only one eigenstate when the upper energy level locates outside the band gap, and atom hardly stays in upper energy level; there are two eigenstates when the upper energy level locates in the band gap, but the properties of the two are quite different each to other. The distribution of particle number on every energy level varies obviously as the driving field parameter varies.

Pieter Kok

Wen-Yuan Wang, Hui Cao, Shi-Liang Zhu +2 more

We investigate the energy levels of a spin–orbit-coupled Bose–Einstein condensate in a double-well potential under the mean-field approximation. We find that the energy levels of the system can be significantly influenced by the atomic interactions. Without atomic interaction, four energy levels change linearly with the tunneling amplitude, the Raman coupling, and the spin–orbit coupling. However, whenever atomic interaction is considered, three more energy levels will appear, which have a nonlinear dependence on those parameters above. These three energy levels are multi-degenerate and related to the macro-symmetry of the system.