In contrast to the classical case, the quantum three-body problem is amenable to qualitative analysis and, in some cases, even to analytic solutions. In 1970, Vitaly Efimov predicted that resonant two-body forces could give rise to a series of bound energy levels in three-particle systems. When the short-ranged two-body forces approached resonance, he found a universal long-range three-body attraction emerging, giving rise to an infinite number of trimer states with binding energies obeying a discrete scaling law at resonance. This oddity in the three-body spectrum close to the zero-energy threshold has since become known as the quantum Efimov effect and the term Efimov physics now covers an array of universal phenomena arising in few-body systems, for particles interacting via short-ranged resonant interactions, whose appearance is due to an emergent three-body attractive force.

In this thesis I aim to summarize the theory of Efimov physics and the methodology used for developing a computer code that calculates the effective long-range three-body potentials, which give rise to the discrete Efimov energy spectrum. The calculations of these potentials were performed by formulating the problem in hyperspherical coordinates and introducing the adiabatic representation where the hyperradius is treated as an adiabatic parameter.