# Energy levels of a 3 dimensional infinite square well

1. Feb 26, 2013

### bobred

1. The problem statement, all variables and given/known data

Calculate the wavelength of the electromagnetic radiation emitted when
an electron makes a transition from the third energy level, E3, to the lowest energy level, E1.

2. Relevant equations

$E_n = \frac{\left (n_{x}^{2}+n_{y}^{2}+n_{z}^{2} \right) \pi^{2} \hbar^{2}}{2m_{e}L^{2}}$

3. The attempt at a solution
Working out the wavelength is not a problem, my problem comes for the values of n for the third level. For the lowest energy level we have

$(1^{2} + 1^{2} + 1^{2})$

My question is for the third energy level is it

$(1^{2} + 2^{2} + 2^{2})$?

Thanks

2. Feb 26, 2013

### TheForce

Yep, as long as they are referring to E3 and not the third excited state in the problem,(E1 is the ground state the way you asked the question). And for your interest you are dealing with a symmetric box so the energy levels are degenerate. Meaning you could take 2,2,1 1,2,2 or 2,1,2. E2 would be 2,1,1, 1,2,1 or 1,1,2. These are called degenerate eigenstates.

3. Feb 26, 2013

### bobred

Thanks that's what I thought.

4. Feb 26, 2013

### TheForce

No problem, I recommend you look into rectangular/square wells to refine your understanding.

Last edited: Feb 26, 2013