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H = l²/2I + F*d*cos theta

where d is the dipole moment. The term F*d*cos theta is small. I write the energy of ground state as

E_0 = \hbar*l*(l+1)/ 2I

Than I have to determine how much the ground-state energy changes as a result of interaction with the field. I have two questions:

1. Is the ground state energy correct - it should not be <psi_0|H|psi_0)?

2. How to proceed using first-order perturbation theory

Thanks in advance