Quantization of the Kepler Problem

Abstract

The expression “quantization of a mechanical system” is somewhat vague and this is not the place to give an exact and precise definition (which, probably’, can not be given at all). So we take it for granted that the reader is familiar with the fascinating subtleties of quantum mechanics and only recall that, from the physical point of view, quantizing the Kepler Problem means to find the spectrum of the energy of the hydrogen atom and the probability distribution of the electron. We will try, in Part II of this book, to make mathematically well defined the term “quantization”, while, in this chapter, we review the historical methods for quantizing the problem, and, more precisely, the Schrödinger, the Pauli and the Fock methods.