 
Summary: Physics 607 Exam 1
Please show all significant steps clearly in all problems.
1. We treated a diatomic molecule as a rigid rotor, but it actually stretches as it rotates
faster. If the rotations are treated classically, we can write
= aL2
 bL4
+ ... (1)
where
a = ¯h2
/2I (2)
and I is the unperturbed moment of inertia. If the rotations are treated quantummechanically,
this becomes
J = a ( + 1)  b 2
( + 1)2
+ ... (3)
where
= 0, 1, 2, ... (4)
is the angular mometum quantum number, with a degeneracy of (2 + 1) since
m =  ,  + 1, ..., 1, 0, 1, ...,  1, . (5)
You may treat the term involving b as very small (since enormous values of L are not regarded
