I have a problem about the interpretation of an exercise.
Given the following Hamiltonian
$$H=\frac{\mathbf{p_0}^2}{2m}+\frac{\mathbf{p_1}^2}{2m}+\frac{\mathbf{p_2}^2}{2m}-2V(\mathbf{r_1}- \mathbf{r_0})+V(\mathbf{r_2}-\mathbf{r_1})$$
where $$V(\mathbf x)=\frac {e^2}{|\mathbf x|}.$$
I have to
enumerate all the continue transformation such as the form of H remains unchanged and match to each one a costant of motion.
I have thought that the form of H remains unchanged for translation and rotation, but I don't know how I can match a constant of motion. Is "constant of motion" linked to "generating function of the transformation"?
