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Projective measurements lead to some weird things. Consider a two level system with basis vectors {Ill}, I1\". We are going to evolve the system according the Hamiltonian H = g? where Y is the Pauli matrix (3 I; ). (a) What is the unitary operator associated with time evolution? Given an initial prepared state of We) = IG}. 1Write an expression for Irt. [b] \"Fhat is the probability, as function of time, to measure ID}? {e} Suppose we study the system over the time interval [II], T] where T 25> at E %. We perform a measurement, in the {In} , |l}} basis, at every time %, %, - -- where N is large. Assuming each measurement is independent from the other, what's the probability that the spin never ips to H}? [d] Evaluate this probability in the limit of N } oo