Are Degenerate Energy Levels the Same as Ground States in Quantum Mechanics?

[Denver Dang]

Hi...

I'm having a little trouble understanding this concept.

An energy level is a level where fx. electrons can be in. Ground state, 1st excited state etc., right ? So if I'm not mistaken, a degenerate state is when two or more different quantum states (Fx. electrons) are in the same energy level ?

Does this mean, for hydrogen at least, that the ground state is not degenerate, since there is only "room" for one electron/state in that level ? And then for the other levels, according to the orbitals of the atom, there are "room" for more states in that perticular energy level ?

I just think I'm a bit confused about this. Not even sure I've asked the right question :)

But I hope for some clarity of some sort :)


Regards

 

[zhermes]

I'm a little lost on what "fx" is, but it sounds like you're on the right track. You wouldn't say that the "ground state of hydrogen is degenerate," but you would say that the two n=1 spin states are degenerate (i.e. spin up and spin down), because they have the same energy. Similarly (for n=2, l=1) you could say the three different p orbitals are degenerate (again, because they have the same energy).

 

[Denver Dang]

Hmmm...

So it's when you have different states, due to different quantum numbers, in the same energy level, you have degeneracy ? So for n,l,m = "Large numbers" you would have a large "multi"-fold degeneracy ?

But what happens when you take fine structure, and hyperfine structuere into account ?
Then you get some small changes, splittings, in energy levels all of a sudden. Does this mean that the n=1 state, for example, is not degenerate anymore, because the small difference in energy levels ? Or have I misunderstood something ? :)


Regards

 

[zhermes]

So it's when you have different states, due to different quantum numbers, in the same energy level, you have degeneracy ? So for n,l,m = "Large numbers" you would have a large "multi"-fold degeneracy ?

It depends on the particular system; but in general: yes, absolutely.

But what happens when you take fine structure, and hyperfine structuere into account ?
Then you get some small changes, splittings, in energy levels all of a sudden. Does this mean that the n=1 state, for example, is not degenerate anymore, because the small difference in energy levels ? Or have I misunderstood something ? :)

It sounds like you've understood it exactly; that's a good question. I think that really just comes down to what you're referring to exactly---People would still often say they're degenerate if they're only referring to the general energy level; at the same time its completely true that the "degeneracy is broken" due to (hyper)fine splitting. So in cases like that its really just a question of reference point/context/etc. Its very possible that saying those energy levels are still degenerate is 'technically' incorrect.

 

[Denver Dang]

Ok... Thank you very much :)