Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: Ho21 Но Where L is the total angular momentum operator, and I is a constant (the moment of 2π) and dr' sin θ d θ d φ. The normalized inertia). Remember (0 θ n; 0 φ eigenfunctions for the -1 state are: Ye(9,9) Je cose A molecule in the I = 1 state is placed in a crystal for which the interaction may be written: Where k is the interaction strength. Determine the resulting energies and sketch the splitting pattern. See attached table of integrals Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: Ho21 Но Where L is the total angular momentum operator, and I is a constant (the moment of 2π) and dr' sin θ d θ d φ. The normalized inertia). Remember (0 θ n; 0 φ eigenfunctions for the -1 state are: Ye(9,9) Je cose A molecule in the I = 1 state is placed in a crystal for which the interaction may be written: Where k is the interaction strength. Determine the resulting energies and sketch the splitting pattern. See attached table of integrals