Constraint quantization: case of the hydrogen atom

The connection between the R3 hydrogen atom and R2 (an operation in a mathematical system indicating the product of two elements) R2 harmonic oscillator or free-particle systems subjected to constraints is studied for the discrete spectrum, the continuous spectrum, and the zero-energy point of the hydrogen atom. This study is conducted in the framework of two complementary approaches: a local (or infinitesimal) approach by bosonization of the Pauli equations and a global (or partial-differential-equations) approach by applying a nonbijective canonical transformation (viz., the Kustaanheimo-Stiefel transformation) to the Schroedinger equation of the R3 hydrogen atom. The case of the hydrogen atom in a uniform electromagnetic field (Stark and Zeeman effects) is also considered