Hyperspherical coordinates provide a systematic way of describing three-body systems. Solving three-body SchrÃ¶dinger 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 H_{3}^{+} and (2) ultracold collisions of three identical bosons.

Hyperspherical coordinates provide a systematic way of describing three-body systems. Solving three-body SchrÃ¶dinger 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 H_{3}^{+} and (2) ultracold collisions of three identical bosons.