2.*Problem 6.9 Consider a quantum system with just three linearly independent states.The Hamiltonian, in matrix form, is0.H = Vo1where Vo is a constant and e is some small number (e « 1).(a) Write down the eigenvectors and eigenvalues of the unperturbed Hamiltonian(e = 0).%3D(b) Solve for the exact eigenvalues of H. Expand each of them as a power series inE, up to second order.(c) Use first- and second-order nondegenerate perturbation theory to find the ap-proximate eigenvalue for the state that grows out of the nondegenerate eigen-vector of H. Compare the exact result from (b).(d) Use degenerate perturbation theory to find the first-order correction to the twoinitially degenerate eigenvalues. Compare the exact results.

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€ 2/ here Vo is a constant and e is some small number (e < 1). (a) Write down the eigenvectors and eigenvalues of the unperturbed Hamiltonian (e = 0). (b) Solve for the exact eigenvalues of H. Expand each of them as a power series ir E, up to second order. (c) Use first- and second-order nondegenerate perturbation theory to find the ap proximate eigenvalue for the state that grows out of the nondegenerate eigen vector of H0, Compare the exact result from (b).

€ 2/ here Vo is a constant and e is some small number (e < 1). (a) Write down the eigenvectors and eigenvalues of the unperturbed Hamiltonian (e = 0). (b) Solve for the exact eigenvalues of H. Expand each of them as a power series ir E, up to second order. (c) Use first- and second-order nondegenerate perturbation theory to find the ap proximate eigenvalue for the state that grows out of the nondegenerate eigen vector of H0, Compare the exact result from (b).