Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S7 / 3 / d / Solution

For $f=F(H)$ with no explicit time dependence, ${\partial }_{t}f=0$ and $[H,F(H)]=F^{\prime }(H)[H,H]=0$. It therefore solves the stationary transport equation. Normalizability and the accessible energy region still have to be checked for a proposed probability distribution.