# Quantum - Electron in an infinite rectangular prism well

1. Nov 16, 2009

### golmschenk

1. The problem statement, all variables and given/known data
If an electron is in an infinite rectangular prism well, with sides of length a, b, and c where c is the shortest and (b^2)*c=a^3, for what value of the d=b/c is the first excited state of the electron minimized? This isn't the complete problem but it's the part that's giving me trouble/

2. Relevant equations
I'm using the equations E=(h^2*pi^2/(2m))*((n_x/l_x)^2*(n_y/l_y)^2*(n_z/l_z)^2) but it's suppose to be used for an electron gas in a solid. The question is referring to a crystal. Is this equation one I want to use? Sorry for not using the correct math notation to make it look nice.

3. The attempt at a solution
My attempted solution is basically just plugging it into that equation.

2. Nov 18, 2009

### lanedance

i'm not that familiar with the equation you give, but don't think its the the correct one to use

the infinite potential rectangular box has a reasonable analytic solution solved through separation of variables (the spatial cartesian variables can be separated in the DE )

you will get a similar equation to the one you quote for energy, however the $\frac({n_x}{L_x})^2$ terms are summed not multiplied

3. Nov 18, 2009

### golmschenk

Oops, yeah, summed is actually what I meant to type. And I think that ended up working out. I don't know for sure that I got the right answer yet, but it seemed to work. Thanks.