A neutron star is composed of a degenerate neutron gas but the neutrons are fermions so they still occupy distinct states. So what is it about the neutron gas that makes it degenerate?
In an atom two electron states are degenerate if they have the same energy. Is this the same degeneracy as in the neutron star or does it have a different meaning?
I guess I’m trying to find out what physicists mean when they say something is degenerate.
Two things are degenerate when they have the same energy. That’s all.
What two things have the same energy in the OP’s first example, the neutron star?
No, that’s not quite right. Degenerate matter is matter in which all available quantum states have been filled. The Pauli exclusion principle won’t allow two particles to exist at the same quantum state, so once all those states have been filled, further compression is prevented.
But in an atom all the lowest available energy states are filled, and an atom isn’t called degenerate. Maybe it means that all the atomic orbitals have been destroyed or collapse or something.
And then there’s still the problem with, “In an atom two states are degenerate if they have the same energy.”
Energy states and quantum states are not the same thing at all. read this article on quantum states. Having the same energy has nothing to do with degenerate matter states.
From ”Introduction to Quantum Mechanics” page 69 by David Griffiths
I’m beginning to think this word is used in two different ways. When dealing with a fermionic gas it means the atomic orbitals have been squashed out of existence and when dealing with normal matter it means two states have the same energy
Okay, let me clarify then, since there’s obviously been some confusion. Two quantum states are degenerate when they have the same energy. The same is true when we talk about classical physics, in fact; degenerate states are states with equal energies.
Now, as to degenerate matter being matter in which all states have been filled… I’m afraid to say that this is not really right, as there are an infinite number of quantum states. The key point is that we have two competing things:
So what’s degenerate about degenerate matter, then? Basically, all the degenerate states are filled. Whence the name, as far as I know. That’s oversimplifying some, but it’s the basic idea.
And what about quark stars?
how degenerate are they?
How low can you go?
Quantum, Arkansas pop. 115
Are you saying that all the states that are filled in a neutron star are degenerate states? Are you saying that all these filled degererate states have the same energy? I’m having a lot of trouble seeing how they could all have the same energy.
No no, I’m not. I am saying that you’ve got a whole bunch of states (an infinite amount, remember?), some of which are degenerate. When you have some degenerate states still available, you don’t really have degenerate matter yet, to the best of my understanding, because you can squeeze on the stuff, and you still have useful states available.
Once all those useful states are filled, which requires filling both the non-degenerate states and all the appropriate degenerate states as well, THEN you’re in trouble.
Think back to the atom for a moment. You have things like the 1s states. Then you have the 2s states. Then all of a sudden you have a whole bunch of 2p states, all of which are degenerate with eachother (ignoring complications for the moment from fine structure and so on). So not all the states are degenerate with all the others, but SOME are degenerate with some of the others.
I could be a bit on the confused side here, I admit; neutron stars aren’t exactly the kinds of things I work with on a day-to-day basis. But I think I’m in the right general ballpark.