Quantum  Electron in an infinite rectangular prism wellby golmschenk Tags: electron, infinite, prism, quantum, rectangular 

#1
Nov1609, 11:47 PM

P: 36

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. Thanks for your time. 



#2
Nov1809, 02:22 AM

HW Helper
P: 3,309

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 [itex] \frac({n_x}{L_x})^2[/itex] terms are summed not multiplied 



#3
Nov1809, 07:14 PM

P: 36

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.



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