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(This is a tricky problem because the degeneracy between the first and the second state is not removed in first order. See also Gottfried (1966), p. 397, Problem 1.) This problem is from Schiff (1968), p. 295, Problem 4. A system that has three unperturbed states can be represented by the perturbed Hamiltonian matrix ( E1 0 a 0 E1 b a^* b^* E2) where E2>E1. The quantities a and b are to be regarded as perturbations that are of the same order and are small compare
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