A quantum particle moving in the potential well with infinitely high walls at x = 0 ,L

1. Oct 14, 2014

tasos

1. The problem statement, all variables and given/known data
(a) Find the energy eigenvalues and eigenfunctions for this well.
(b) If the particle at time t = 0 is in state Ψ = constant (0 <x <L)). Normalize this state.
Find the state that will be after time t>0

(c) For the previous particle, if we measure the energy at time t = 0, what is
probability the particle is in the ground state of the well;
If the same measurement made on time t>0, whats the probability of particle to be at the ground state?

(e) For the particle of the question (b) What is the probability density to find the particle at
x = L / 2 at time t = 0.

(g) At the time t = 0, we measure momentum of the particle and it is found to be q. What is
probability after time t,that the particle is located in n-th energy level.

Im getting some difficulties when im trying to calculate the last sub-question .
I've thought that i have to Expand the eigenfactions of momentum in the linear combination of the ones of the Hamiltonian ( Given by the TDSE) And then re-expand the result back to the momentum space in order to see what happens as n-> infinite ..
(Im thinking this in order to make the momentum eigenfunction timedepedent.)

2. Relevant equations

3. The attempt at a solution

2. Oct 19, 2014