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Question: 1 the hamiltonian for some two level system is h...

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1. The Hamiltonian for some two level system is H =C where C is a constant with dimensions of energy (a) Find the energy eigenvalues and normalised eigenvectors for this system. Show that the eigenvectors are orthogonal If the system is described by the state function function at some later time t (4 marks) (b) at t =0 write down the state 0 (2 marks) (c) If Ei and E2 are the energy eigenvalues where E> E2, and the system is initially in the scalculate the probability that a measurement of energy yields the value Ei at any time What is the expectation value of the system energy? If the system is subjected to a time independent perturbation described by 0 (I mark) (d) (I mark) (e) -0.1 0 0 0.1 н с calculate a first order approximation for the new energy levels of the system. (2 marks)

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