A parallel derivation of the Boltzmann equation in both classical and quantum mechanics is given. In particular, a quantal form which closely resembles the classical form is obtained;The kinetic theory appropriate to the thermal conductivity, thermal diffusion, and diffusion coefficients is given in both classical and quantum mechanics for an atom and diamagnetic diatom (more generally, a linear molecule) mixture in an applied magnetic field. Explicit expressions for energy dependent, and thermally averaged cross sections are obtained;A study of the effect of chattering collisions on various thermally averaged cross sections is given for a rigid potential. It is found that some cross sections are more strongly affected than others. In particular, those cross sections which are related by energy conservation are most strongly affected. The applicability of a rigid interaction as a control variate in a Monte Carlo study of a realistic interaction is discussed in light of these results;Selected cross sections are evaluated via a Monte Carlo technique and a quantum mechanical sudden approximation (IOS) for realistic Ar-CO(,2), He-CO(,2), and Ar-N(,2) interactions. These results are compared to experiment whenever possible and are used to evaluate the applicability of various IOS labeling schemes. In conclusion, earlier work due to Verlin et al.('1) is evaluated in light of these results with particular emphasis on the neglect of chattering;('(DBLDAG))DOE Report IS-T-955. This work was performed under ContractW-7405-eng-82 with the Department of Oil, Gas, and Energy;('1)Verlin, J. D., et al., J. Chem. Phys. 62, 4146-4150 (1974).