Suppose i release a particle at (x=a,y=0) with (p_x = b, p_y = 0) and you release one in the transformed state (x=0, y=a) with (p_x = b, p_y = 0) where the transformation is that we rotate the coordinates but not the momenta. This is a non canonical transformation that leaves H invariant. Show that at later times the states of the two particles are not related by the same transformation. i am not sure what to do on this problem. i can intuitively see that if the acceleration is 0, both particles move to the right at a constant velocity of p_x / m but i am not sure how mathematically describe the transformations of the two particles through time and show that they are different. can anyone give me some pointers? thanks.