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Question 1b (1.5 pts). Project the CID Schr¨odinger equation on the left by hΦ| and hΦabij | to obtain expressions for Ec and cijab.
Question 1c (5 pts). Use Wick’s theorem to evaluate each matrix element obtained in part b. You do not have to convert the KM contraction dots into η’s and γ’s, nor do you have to expand the index antisymmetrizers Pˆ. For example, an acceptable place to stop for your answer would be something like

Question 2 (3 pts). Explain in your own words how perturbation theory works, as applied to the timeindependent Schrodinger equation. Be sure to include a brief discussion of the following in your answer: • the Hamiltonian
• λ
• The perturbation expansion
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Question 3 (3 pts). Derive an expression for Φ0 by explicitly pulling out terms from the perturbation expansion using the resolvent formalism. Explain you steps.
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Question 4 (2 pts). Derive Φ0 using the energy substitution trick.
Question 5 (2 pts). Derive an expression for using L¨owdin’s PT formalism.
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