# Degeneracy in Quantum Mechanics

1. Jul 31, 2011

### 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 text books or anywhere online. And how does something have infinte degeneracy?

2. Jul 31, 2011

### Bloodthunder

3. Jul 31, 2011

### nnnm4

When you solve the Schrodinger 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.)