THE THREE-BODY PROBLEM
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THE THREE-BODY PROBLEM book
Systems of many particles are common in nature. The complexity of the corresponding quantum mechanical problem increases rapidly as the number of particles increases. We have seen that it is possible to deal with two-body quantum systems effectively by transforming to center-of-mass coordinates, at least within the framework of non-relativistic quantum mechanics. The complexity of the problem increases enormously when we consider systems of three particles. Not only are we dealing with an expanded phase space, but also the task of selecting, out of many possibilities, the correct variables to describe the system. Among the important three-body systems that require a quantum mechanical treatment are the triton (bound state of two neutrons and a proton), the Helium atom (bound state of two electrons and a point nucleus) and numerous nuclear and atomic scattering events in which three particles participate. Despite the complexity of the problem, considerable progress has been made. This chapter describes some approaches to the three-body bound state problem in quantum mechanics.