I have two similar questions. 1. Show the relationship between invariancy of hamiltonian to translation and conservation of momentum. (In QM) 2. Show the relationship between invariancy of hamiltonian to rotation and conservation of angular momentum. (In QM) I have no idea how to prove this. I was wondering if I could use Heisenberg operator equation on momentum operator so I could prove that operator doesn't change with time, but I don't how to input hamiltonian invariancy to translation in equation and even then is that the real way of doing it.