4. Question 4 - Matrix eigenvalues/eigenvectors (16 marks) Assume there is a linear variational problem described by the Hamiltonian matrix (where a ? 0): H? = ? ? a 1 0 1 a 1 0 1 a ? ? a) Find the eigenvalues of H? in terms of the constant a. Show all relevant work/steps. What is the ground state energy if a = ? 2?

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