Metaplectic-c Quantized Energy Levels of the Hydrogen Atom

Abstract

This paper calculates the quantized energy levels of the hydrogen atom, using a metaplectic-c prequantization bundle and a definition of a quantized energy level that was introduced by the author in a previous paper [9]. The calculation makes use of a computational technique also demonstrated in that paper. The result is consistent with the standard quantum mechanical prediction. Unlike other treatments of the hydrogen atom, this approach does not require the construction of the symplectic reduction, but takes place over a regular level set of the energy function. The Ligon-Schaaf regularization map is used to transform the problem into one of determining the quantized energy levels of a free particle on T S 3 .