Can someone explain the idea of degeneracy of orbitals?

[eccles1214]

This is a confusing topic. What does it mean to be degenerate?
How does this apply to atomic orbitals versus molecular orbitals?
Can you point me to a good reference book on the subject?

 

[G01]

The concept of degeneracy is related to the energies of the different quantum states of a system. A given system is said to be degenerate if more than one eigenstate has the same energy as an eigenvalue. Take the hydrogen atom as an example:

In the H atom there are different energy levels and within each energy level you have an orbital corresponding to different allowed values for the electron's angular momentum. These orbitals are the eigenstates for the electron bound to the proton.

There is only one orbital(eigenstate) which has the ground energy as an eigenvalue. This is the S orbital for n=1. Thus, the n=1 energy is non degenerate since there is only one eigenstate the electron can be in (the s orbital) and have that energy.

Now, consider the n=2 energy for hydrogen. Any electron in the s orbital state or one of the p-orbital states will have this energy. Thus, the n=2 energy is said to be degenerate since an electron can have this energy and be in a multitude of different eigenstates of the system.

That is an example of degeneracy in an atomic system. As for a molecular system, I think it is best if i left that to someone else. I have not yet covered that in any class, so I would not be the person to ask.