A particle is confined to a one-dimensional box. The ends of the box move slowly towards the middle. By slowly we mean the speed of the ends is small when compared to the speed of the particle. Solve the following using Lagrangian formulation and then using the Hamiltonian.
(a) if the momentum of the particle is p0 when the walls are a distance x0 apart, find the momentum of the particle at any later time assuming the collisions with the wall are perfectly elastic. Also assume the motion is nonrelativistic at all times.
(b) When the walls are a distance x apart, what average external force must be applied to each wall in order to move it at a constant speed?