Problem 4. The Hamiltonian Ho for a two level system can be written in matrix form as Но — (0)- E and the corresponding eigenfunctions are simply given by lo") = (6). lo) = () lø0) = (H) A perturbation of the form H1 = is added, resulting in H = Ho + H1. (a) Solve the problem exactly to find the energies and eigenstates of H. (b) Solve for the energies of H using time-independent perturbation theory up to second order and com- pare your answer with your exact result. (Assume A«JE®) – E,).
Problem 4. The Hamiltonian Ho for a two level system can be written in matrix form as Но — (0)- E and the corresponding eigenfunctions are simply given by lo") = (6). lo) = () lø0) = (H) A perturbation of the form H1 = is added, resulting in H = Ho + H1. (a) Solve the problem exactly to find the energies and eigenstates of H. (b) Solve for the energies of H using time-independent perturbation theory up to second order and com- pare your answer with your exact result. (Assume A«JE®) – E,).
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Transcribed Image Text:Problem 4. The Hamiltonian Ho for a two level system can be written in matrix form as
(0)
Ho =
»(0)
E
and the corresponding eigenfunctions are simply given by
lo") = (6), l") = (4)
A perturbation of the form
H = C A)
is added, resulting in H = Ho + H1.
(a) Solve the problem exactly to find the energies and eigenstates of H.
(b) Solve for the energies of H using time-independent perturbation theory up to second order and com-
pare your answer with your exact result. (Assume A « [E,º – E).
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