For a diatomic molecule the Hamiltonian is equivalent to that of a particle-on-a

Question

For a diatomic molecule the Hamiltonian is equivalent to that of a particle-on-a-sphere, and is more involved than the particle-on-the-ring. Nevertheless, the expression for the allowed energy levels is easy to remember, because it is analogous to the classical expression: E_Rot = j^2/2I, where J is the classical angular momentum vector. All we have to do to get the quantum expression is replace the classical angular momentum squared with its quantum mechanical analog (J^2) = J(J + 1)h^2, where J is the angular momentum operator, and J is angular momentum quantum number. Write down the expression for the quantized energy, E_j, indicate the possible values of J as well as the degeneracy of each level.

Explanation / Answer

Solution:

Ej= (h^2/(8 pi^2I))J(J+1)

Ej = BJ(J+1) where B = h/ 8 pi^2 Ic

if j =4 E4 = 20 B

j= 3 Ej= 12B

j==2 => Ej = 6 B

j= 1 => Ej = 2B

J=0 => Ej = 0

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