The Hamiltonian of a system with n degrees of freedom is given by \(H(q_1,q_2,...,p_1,p_2,..,t), \) with an explicit dependence on the time t. Which of the following is correct?
1
Different phase trajectories cannot intersect each other.
2
H always represents the total energy of the system and is constant of the motion.
3
The equations \(\dot{q}_i =\frac{\partial H}{\partial p_i} , \dot{p}_i = - \frac{\partial H}{\partial q_i}\) , are not valid since H has explicit time dependence.
4
Any initial volume element in phase space remains unchanged in magnitude under time evolution.
5
Question Not Attempted