# Particle in a box question

1. Feb 21, 2006

### allanm1

"Particle in a box" question

The solution of Schrodingers equation for the simple "particle in a box" problem is:

E = (n^2)(h^2) / 8m(L^2)

where L = the length of the box.

See http://en.wikipedia.org/wiki/particle_in_a_box" [Broken]

Say that the initial energy of the particle is E1.
If at a later time the length of the box is changed (a moveable wall), then there are now a completely new set of possible energies available, for n=1,2,3 etc. What if none of these new allowed energies equals the original energy of the particle?

What happens to the energy difference?

Last edited by a moderator: May 2, 2017
2. Feb 21, 2006

### quasar987

3. Feb 21, 2006

### Physics Monkey

It depends on how slowly the walls of the box are moved.

4. Feb 21, 2006

### quasar987

Suppose they are abruptly removed. I.e. they instantly vanish. The particle state is now in a superposition of the eigenstates of the new box and will settle into one of them upon measurement. In any case, the energy upon measurement wil be different than originally.

5. Feb 22, 2006

### allanm1

Particle in a box

In my original question I was assuming that the energy of the particle was
conserved after changing the size of the box.

Was I wrong in assuming this. Maybee changing the size of the box does work on the particle? Like compressing a gas if there were many particles.

Is it the energy state n that is conserved?