Homogeneous gravity field time evolution position and momentum operato

[VVS]

Homework Statement

I am trying to solve Problem 21 from this sheet:
View attachment T2SS14-Ex7.pdf

Homework Equations

The equation describing the time evolution of operators is given in the problem.

The Attempt at a Solution

I have found the commutators of the position and momentum operator with the Hamiltonian.
View attachment Übung 21_3.pdf
I don't know how to do the rest of the exercise.

 

[Simon Bridge]

(a) See equation (5) relating the commutator to the time evolution to get $\hat X(t)$ and $\hat P(t)$
(b) follows from there.