I was given a few Quantum questions, and they're all math related. Not sure how many understand this, but it was worth a shot.

Given that a free electron is contained in a box described by the wave function and with walls located at and , answer the following:

1.) Find the wave function at any time .

2.) Determine all possible energy measurements and determine the probability at which they occur.

3.) Find the wave function after a measurement of energy given that that energy gives ground state energy.

4.) Determine using the results from 2.). Then, using the result from 1.), find

5.) Suppose suddenly that the wall moved from to , determine the probability that the electron is located in the 3rd energy state of this box.