**Dimensional Scaling for Atoms and Molecules (PHAS colloquium)** - Goong Chen

E. Witten (Field medalist 1990) first suggested this idea in 1980. He was motivated by quantum chromodynamics. His idea is to imbed the Laplacian operator corresponding to the kinetic energy in the Schrodinger equation into a much higher dimension D, by regarding each dimension as a ``color'', and then let D tend to infinity. By a heuristic argument, Witten derived the ground state energy of the hydrogen atom with about 60% error.
D. Herschbach (Nobel laureate 1986 in chemistry) refined Witten's argument and developed his ``hydrogenic D-scaling'' method and then obtained the exact ground state energy of the hydrogen atom. One of the great advantages of D-scaling is that the need to solve partial differential equations can be avoided.
In this talk, we will first give a quick introduction of the Schrodinger-Born-Oppenheimer model for simple atoms and molecules. We then show how the D-scaling arguments work for the hydrogen atom. We then proceed to derive the ``old Bohr model'' through D-scaling a la papers of Svidzinsky-Scully-Herschbach, showing that the Bohr model is actually fully quantum mechanical in an asymptotic sense. We then indicate how to estimate the energy levels of excited states. Numerical data will be compared with the experimental data to show the agreements and deviations, and indicate some future directions for research.