I think probability in low velocity region should depend on v0-v1 (the closer they are together, the longer the time particle spends in low velocity region).
My reasoning is: if you look at v(t)=v0-v1*Cos(w*t), particle's velocity oscillates around v0, and Cos function is symmetric in t...
Probability to find a particle in some region of space is inversely proportional to velocity particle has in that region of space.
Let's say we have two cases: one particle has velocity given by v(t)=v0*Cos(w*t), and other by v(t)=v0-v1*Cos(w*t), (v0>v1).
Since particle spends more time in...