Abstract
Transition state theory as developed for chemical reactions is transferred to ballistic electrons. The phase-space flux through the transition state is related to the conductance. Steps in the conductance follow from a semiclassical extension of this formula. Tunnelling corrections have to be included to yield the rounding of the steps. A magnetic field causes a sharpening of the steps and at finite temperature an additional broadening. The calculation also shed some light on the abilities and limitations of the semiclassical approach.