Degeneracy in Quantum Mechanics

[hc91]

Can anyone explain to me what Degeneracy is properly. I know its something to do with having different eigenvalues on the same energy level or something like that, but have not been able to find a good explanation in any textbooks or anywhere online. And how does something have infinite degeneracy?

 

[Bloodthunder]

It just means that 2 or more quantum states are at the same energy level. This can be seen in bosons, as opposed to fermions which are non-degenerate.

A few links to help.
http://en.wikipedia.org/wiki/Degenerate_energy_level
http://en.wikipedia.org/wiki/Boson
http://en.wikipedia.org/wiki/Fermion

 

[nnnm4]

When you solve the Schrödinger Equation for a particular potential, you sometimes get different states that have the same energy. For example consider a particle in a 3D box. The energy is labeled by 3 quantum numbers (nx, ny, nz). The 3 numbers are equivalent so (2 1 1), (1 2 1), and (1 1 2) are three independent quantum states that have the same energy. It is said they are degenerate. Notice that because the states are linearly independent, you can have fermions at the same energy because one can occupy each on of these states (if you include spin, then two fermions can actually occupy each one of those states, so spin doubles the number of degenerate states if it does not appear in the hamiltonian.)