What Happens to the Wave Function When the Size of a Quantum Well Doubles?

[chaotic]

Homework Statement

there is a infinite quantum well with size L and there is a particle in it with mass m. suddenly the size of the quantum well is doubled. What will be the wave function at a later time t ?

Homework Equations

ψ= $\sqrt{2/L}$ sin (n pi x / L)

E = n^2 pi^2 h^2 / 2mL^2

The Attempt at a Solution

do we need to find c_n again with 2L ?

 

[Simon Bridge]

Yes.
I'd normally do this by expressing the initial state of the particle, in the 1L well, in terms of a superposition of states of the final 2L well... then finding the time-evolution of those states.

I'd have expected the initial state to be a specified n state (i.e. the ground state).

A lot depends on context - eg.
If there is a mechanism for decay present, then the question could be answered in terms of the energy lost in the decay from initial to final states. (Otherwise the system remains in a composite state until some measurement of energy is made.)