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The rigid rotor is a simple model of a rotating diatomic molecule. We
consider the diatomic to consist of two point masses at a fixed
internuclear distance. We then reduce the model to a one-dimensional
system by considering the rigid rotor to have one mass fixed at the
origin, which is orbited by the reduced mass ,
at a distance r.
The Schrödinger equation is (cf. McQuarrie ,
section 6.4 for a clear explanation)
After a little effort, the eigenfunctions can be shown to be the
PJ|M|(x) are the associated Legendre functions.
The eigenvalues are simply
Each energy level EJ is 2J+1-fold degenerate in M, since M can