- #1
tasos
- 9
- 0
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.)