Infinite Quantum Well: E2-E1, Wavefunction, Energy

[grothem]

Homework Statement

An infinite quantum well width is 5 nm. An electron is confined in the well with 50% in the lowest eigenstate E1 and 50% in the second lowest state E2.
1. What is the energy difference between the two lowest states, E2-E1
2. What is the possible wavefunction of the electron
3. What is the average energy of the electron
4. When t=(Pi/2)[hbar/(E2-E1)], what is the wavefunction

Homework Equations

The Attempt at a Solution

I know the possible wavefunction could be Psi(x)=Sqrt(.5)Phi1(x) + Sqrt(.5)Phi2(x)
And the average energy, .5E1+.5E2
But I'm not sure where the width of the well comes into play for these equations, unless I'm not on the right track

Also, not sure how to find the difference between the two states

 

[gabbagabbahey]

Both \psi_1(x) and \psi_2(x) depend on the width of the well...what are the expressions for these states?

You should also already be familiar with the energy levels of a particle in a box...what are they?