Hyperspherical Approach to Quantal Three-body Theory

<p>Hyperspherical coordinates provide a systematic way of describing three-body systems. Solving three-body Schrödinger equations in an adiabatic hyperspherical representation is the focus of this thesis. An essentially exact solution can be found numerically by including nonadiabatic couplings using either a slow variable discretization or a traditional adiabatic method. Two diff erent types of three-body systems are investigated: (1) rovibrational states of the triatomic hydrogen ion H₃⁺ and (2) ultracold collisions of three identical bosons.</p>