Verallgemeinerte Boltzmann-Gleichung für mehratomige Gase

Abstract

A generalized quantum mechanical Boltzmann equation is derived for the one particle distribution operator of a dilute gas consisting of molecules with arbitrary internal degrees of freedom. The effect of an external, time-independent potential on the scattering process is taken into account. The collision term of the transport equation contains the two-particle scattering operator T and its adjoint in a bilinear way and is non-local. The conservation equations for number of particles, energy, momentum and angular momentum as well as the H-theorem are deduced from the transport equation. One obtains the correct equilibrium distribution operator even in the presence of an external field (e. g. for particles with spin in a homogeneous magnetic field). Some special cases of the generalized Boltzmann equation are discussed treating position and momentum of a particle as classical variables but characterizing the internal state of a molecule by quantum mechanical observables. Using the local part of the collision term only and considering molecules with degenerate, but sufficiently separated internal energy levels one arrives at the Waldmann-Snider equation, which in turn comprises the Waldmann equation for particles with spin and the Wang Chang-Uhlenbeck equation. Special attention is drawn to the case of particles with spin in a magnetic field. Finally, for particles with spin, the local conservation equation for angular momentum, i.e. the Barnett effect (magnetization by rotation) and the antisymmetric part of the pressure tensor are derived from the generalized Boltzmann equation with non-local collision term.