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Suppose that a given Hamiltonian system has two eigenstates |ε1> and |ε2>) where εi, denotes the eigenstate energy with ε2 - ε1 > 0. At time t = 0 the state vector for the system has the form
ψ(t = 0) = (|ε1> + |ε2>)).
(a) Write the form of the state vector at times t > 0.
(b) What is the probability of finding the particle in state |ε2> as a function of t?
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