PROBLEMS
5.1 Consider a system of particles uniformly distributed in space, with a constant particle number density no, and characterized by a velocity distribution function f(v) such that
f(v)=K0    for    \Vi\ <v0    (i = x,y,z)
f(v) = 0 otherwise,
where Kq is a nonzero positive constant. Determine the value of Kq in terms of no and v0.
5.4 Consider the motion of charged particles, in one dimension only, in the presence of an electric potential V(x). Show, by direct substitution, that a function of the form
f = f{imv2 + qV) is a solution of the Boltzmann equation under steady-state conditions.
5.8 Consider a one-dimensional harmonic oscillator whose total energy can be expressed by
E = \{mv2 + cx2)
where c is a constant and x its displacement coordinate. Show that the trajectory described by the representative point of the oscillator, in phase space, is an ellipse.