Another feature of the quantum picture is that state space is not continuous but consists of finite ``raster elements'': just think of the discrete states of an ideal quantum gas. Finally, it depends on the ``symmetry class'' of the particles how many of them may inhabit the same discrete microstate. Fermions, with a wave function of odd symmetry, can take on a particular state only exclusively; the population number of a raster element in pahese space can be just or . In contrast, even-symmetry bosons may in any number share the same microstate.
What are the consequences of these additional counting rules for Statistical
Thermodynamics? To seek an answer we may either proceed in the manner
of Boltzmann (see Section 2.2) or à la Gibbs (see
Chapter 4). For a better understanding we will here sketch both