Hey, trying to remember how to relate the orbital/energy level of an electron to the quantum numbers.

An electron in the 2s state for hydrogen would have n=2 and l=0 right?

4/19/2007 1:56:19 AM

yes

4/19/2007 2:15:41 AM

Alright, now here's the hard one. Does emission by dipole radiation allow for changes in the "n" quantum number? Or does that require quadripole approximation?

4/19/2007 2:22:18 AM

well shit

my gut says quadripole cause i don't know off the top of my head

4/19/2007 2:36:07 AM

Alright because the selection rules say change in l must be +/-1 and change in m can be +/- 1 or 0. Does this imply that change in n is not allowed, or that it isn't restricted?

4/19/2007 2:45:22 AM

pretty sure change in n can't be done

4/19/2007 3:20:41 AM

agreed

4/19/2007 3:27:02 AM

Upon doing some further reading, the n transition is not in doubt and is allowable with dipole radiation approximation. The thing I'm not sure about is the 2p->2s transition. This doesn't seem to violate the selection rules but I had forgotten that the 2s state is HIGHER energy than the 2p state! That means it's not something that will happen happen with this kind of spontaneous emission.

Therefore, the only transitions I have to calculate are the various 2p-> ground state transitions! These are simple since the matrix elements mostly go to zero and I've already had to figure out the nonzero elements. W00t.

Also, just to note, the 2s-2p transition occurs as an intermediary in the 2s-2p-1s transitions, but those require quadrapole approximations and result in 2 photons being emitted. Since I'm actually calculating the energy level lifetimes, this transition would be negligible anyways. This is because the transition probability is a function of the cube of the energy difference. The lamb shift energy difference between the 2p and 2s states is on the order of 10^-6 eV while the 2s/p and 1s energy levels differ by whole eV's.

[Edited on April 19, 2007 at 3:50 AM. Reason : ]

4/19/2007 3:44:01 AM

i gotta re-learn a lot of this

4/19/2007 9:01:56 AM

representation theory ftw

4/19/2007 12:25:16 PM