Energy Conservation in an expanded 1D box

[dLo R6]

I am fairly new to QM and am learning many of the basics right now. We were just discussing conservation of operators (energy, momentum, etc) and I recalled a problem proposed in my textbook about a 1D particle in a box of length L. at a time t, the box suddenly expands to t=2L, in which time the wavefunction does not have time respond. it asked if energy (more specifically, <H>) was conserved during the time that the wall moves.

i'm assuming that the laws of conservation aren't broken and that the Hamiltonian does not change. but then does the fact that the box expanded at a specific time, mean that then the potential V(x) is now a function of time? so then is energy is not conserved since I have to consider the potential in the Hamiltonian now?

 

[dLo R6]

OK now I'm assuming that since the box changes, the potential does change and thus <H> is not equal to <H'>. Is this correct?

 

[Avodyne]

That's correct. An external force moved the wall, doing work on the system, so the energy of the system is not conserved.

 

[flatmaster]

Yes, technically your potential is now a function of time, but you don't want to solve the time-dependent Schrödinger equation. Because the wavefunction doesn't change, Your old wavefunction is a superposition of your new set of wavefuncitons describing your new ISW potential.