To get the dynamics of particles in a box. You are supposed to get the Hamiltonian which is potential energy plus kinetic energy. But does the potential energy take into account the momentum of the particles in the box? What happens if you change the momentum of the particles.. do the potential changes too? And what would happen if you don't solve for the Hamiltonian (or potential plus kinetic energy) but only momentum of the particles in the box.... from the momentum alone.. can you get the potential?