# Particle in a 3D Box

by eep
Tags: particle
 P: 227 Hi, This comes from Griffiths Intro to Quantum Mechanics Prob. 4.2 We're asked to solve an infinite cubical well, which I have no problem with. The next part asks you to call the distinct energy levels E1, E2, E3... etc. in order of increasing energy and determine their degeneracies. It then asks what the degeneracy of E14 is and why is this case interesting. I think the degeneracy of E14 is 6, however I don't see why this case is interesting.
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P: 3,017
 Quote by eep Hi, This comes from Griffiths Intro to Quantum Mechanics Prob. 4.2 We're asked to solve an infinite cubical well, which I have no problem with. The next part asks you to call the distinct energy levels E1, E2, E3... etc. in order of increasing energy and determine their degeneracies. It then asks what the degeneracy of E14 is and why is this case interesting. I think the degeneracy of E14 is 6, however I don't see why this case is interesting.
I seem to recall something special about that level. What are the possible values of the quantum numbers giving that energy?

If two of the three quantum numbers of a certain state are eqaul to one another but different from the third, one expects a 3-fold degeneracy (like 112, 121, 211). If the three quantum numbers are different, one expects a 6-fold degeneracy (123, 132, 213, 231, 321, 312). But there was something special about that state. (Does E14 means that n_x^2 + n_y^2 +n_z^2 = 14? or is it the 14th energy level?)

Patrick
 P: 227 It's the 14th energy level. I have the quantum numbers as (4,3,1).
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P: 3,017
Particle in a 3D Box

 Quote by eep It's the 14th energy level. I have the quantum numbers as (4,3,1).
I tried to verify that this was the 14th energy level but this seemed to be the 12th one to me...But I might have missed a couple. There is nothing special about that one, no.

Pat
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P: 3,017
 Quote by nrqed I tried to verify that this was the 14th energy level but this seemed to be the 12th one to me...But I might have missed a couple. There is nothing special about that one, no. Pat
oops, I find that it's the 13th...

I probably missed one

111

211 plus permutations

221 plus perms..

222

311

321

322

331

332

411

421

422

431