The Quantum Three-body Problem: Baryons and Glueballs as Pivotal Examples

This document contributes to the study of three-body problems in quantum mechanics. Starting from the basic formalism of many-body quantum mechanics, two approximation methods are described, enabling the reader to develop independence in applying this framework. The first method, known as the oscillator bases expansion, allows for the precise solution of various systems, although it requires a rather elaborate implementation. The second method, the envelope theory, offers a more straightforward, albeit approximate yet reliable, evaluation.
The text then turns to specific applications of this formalism in hadronic physics. After reviewing the historical context and introducing the essential features of hadron structure, the aforementioned techniques are used to construct a model that reproduces the baryon spectrum. In the final part, this model is refined by reintroducing relativistic considerations, thereby extending the discussion to a more exotic class of hadrons known as glueballs.