For $f=F(H)$ with no explicit time dependence, $\partial_t f=0$ and $[H,F(H)]=F'(H)[H,H]=0$. It therefore solves the stationary <transport equation>. Normalizability and the accessible <energy> region still have to be checked for a proposed <probability distribution>.

Solution

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

 Solution (source code)