Solving Particle Motion in a Rigid Box: t=0

[Svyatoslav]

I have question, how can I solve problem of particle in rigid box when one of the wall gets completely destroyed? At time t = 0 the right wall of box gets completely destroyed, left wall is still here( ψ(0) = 0 ), also at t = 0 we know that particle is in ground state.
How can I search for evolution ψ(x, t)?

 

[Christopher Grayce]

Expand the t=0 wavefunction (presumably the g.s. of a particle in a box) in free particle plane waves with positive momentum and having a node at the left wall.

 

[Orodruin]

Expand the t=0 wavefunction (presumably the g.s. of a particle in a box) in free particle plane waves with positive momentum and having a node at the left wall.

Due to the wall, there is no translation symmetry and momentum is not a good quantum number. However, momentum squared is. Combining eigenfunctions of positive and negative momentum you can get eigenfunctions of the Hamiltonian that satisfy the appropriate boundary condition.