Theoretical techniques are developed to solve the coupled Schrodinger equations that describe cold magnetically trapped alkali atom dynamics. In particular, a multichannel quantum defect formulation is presented to separate cleanly the atomdependent from the atom-independent contributions to the final scattering matrices. The resulting approach provides a more comprehensive understanding of cold alkali collisions and improves substantially on the efficiency of calculations. Improved Rb two-body interaction potentials are extracted from measured ^{87}Rb inelastic collision rates and from the measured position and width of a ^{85}Rb Feshbach resonance. Using these state-of-the-art potentials, specific atomic hyperfine states have been identified whose collisional properties suggest intriguing possibilities for interesting and novel degenerate gas studies. In addition, a detailed analysis of ^{39}K photoassociation lineshapes has permitted the determination of accurate two-body interaction potentials for this atom as well. Finally, three-body recombination of doubly polarized trapped atoms is investigated. Two qualitatively different mechanisms which control the recombination rate are identified for positive and negative two-body scattering lengths\ α. Surprisingly, the recombination rate is found to scale approximately as α^{4} in both cases.

Theoretical techniques are developed to solve the coupled Schrodinger equations that describe cold magnetically trapped alkali atom dynamics. In particular, a multichannel quantum defect formulation is presented to separate cleanly the atomdependent from the atom-independent contributions to the final scattering matrices. The resulting approach provides a more comprehensive understanding of cold alkali collisions and improves substantially on the efficiency of calculations. Improved Rb two-body interaction potentials are extracted from measured ^{87}Rb inelastic collision rates and from the measured position and width of a ^{85}Rb Feshbach resonance. Using these state-of-the-art potentials, specific atomic hyperfine states have been identified whose collisional properties suggest intriguing possibilities for interesting and novel degenerate gas studies. In addition, a detailed analysis of ^{39}K photoassociation lineshapes has permitted the determination of accurate two-body interaction potentials for this atom as well. Finally, three-body recombination of doubly polarized trapped atoms is investigated. Two qualitatively different mechanisms which control the recombination rate are identified for positive and negative two-body scattering lengths\ α. Surprisingly, the recombination rate is found to scale approximately as α^{4} in both cases.