Rotational Energy and Degeneracy

  • Thread starter pyroknife
  • Start date
I have a question regarding the rotational energy equation, derived based on the rigid rotor assumption:

##\epsilon = k\theta_r J (J+1)##
where k = boltzmann constant, and J is the rotational quantum number.

The degeneracy is 2J+1.

Let's assume the constant quantity ##k\theta_r## = 1 and that the energy level is 2Joules.
Thus 2 = J(J+1) => J = +/- 1. The only physical solution is J = 1.
Thus degeneracy is 3 for J = 1.

Here is where I am confused. I thought degeneracy is when you have an energy level that DOES NOT consist of a unique set of quantum numbers. So if the degeneracy is 3, doesn't that mean I should have 3 different J values that can give me an energy level of 2 Joules?
I think I am understanding this incorrectly, because for 2 joules, the only solution is J = 1. Doesn't that mean the degenearcy is 1?


There are three different and linearly independent solutions to the Schrodinger equation with ##J=1##. That's where the three-fold degeneracy comes from.

Google for "spherical harmonics" to see how this can be; the three solutions are multiples of the three functions ##Y^1_m## with ##m## equal to -1, 0, or 1.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads