If the region ABCD is the phase space region at time time t = 0 , find the region $A'B'C'D'$ at time t given the Hamiltonian is $$ H\,=\,\frac{p^2}{2m}\,-\, m a q $$ and explicitly verify that the area is constant. Take the coordinates of A,B,C and D as $(q_A,p_A)\,,\,(q_B,p_A)\,,\,(q_B,p_C)$ and $(q_A,p_C)$ respectively. |
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