For a noninteracting gas of N particles in a cubic box of volume V = L, where L is the length of the side of box, find the solution, p(p, q, t), of the Liouville equation at time t, where pN = (PPN) and q = (q1,..., qv) with Pi (Pix Piy, Piz) and q (qix, qiy qiz). Assume periodic boundary conditions, and assume that the probability density at time t = 0 is given by

Transcribed Image Text:

3N P(p q3,0)= 71 2L 3N N II II i-10=x,y,z e-p Sin (Tzia) for 0qia L.