Finding Energy Eigenvalues and Eigenfunctions for a Particle Well

[tasos]

Homework Statement

(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, what's 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.
What is the answer if the measurement made 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 I am 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.)

Homework Equations

The Attempt at a Solution

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?