A rigid rotor has two particles of mass m attached to the ends of a massless...
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A rigid rotor has two particles of mass m attached to the ends of a massless rigid rod of length a. The rotor is free to rotate in three dimensions about the center of mass. This is a model for the rotational motion of a homonuclear diatomic molecule, a molecule with two identical nuclei. (An example is 16O2.)
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(a) By expressing the Hamiltonian in terms of the orbital angular momentum, show that the allowed energies of this rigid rotor are of the form
El =h^2*l(l + 1)/ma^2
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(b) What are the normalized eigenfunctions? What is the degeneracy of the lth level?
(c) Consider now the effects of exchange symmetry on the system. Suppose the nuclei are identical fermions. What is the rotational ground state energy and wave function? Consider also the case of two identical bosons.
Homework Answers
Answer:
Note: In the following answer please Replace 'R' and 'L' with "a" and "n" respectively. You will arrive at answer for part-a)
ask part-b and c separately. Thank you.
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