(4) Consider a system described by the Hamiltonian H, H = 0 a a0 !,
where a is a constant. (a) At t = 0, we measure the energy of thesystem, what possible values will we obtain? (b) At later time t,we measure the energy again, how is it related to its value weobtain at t = 0 ? (c) If at t = 0, the system is equally likely tobe in its two possible states, write down the most general state ofthe system at t = 0. (d) What is the probability that at time t =5, the system will be in a state different from its initial state?.(e) Suppose the above Hamiltonian describes a spin-1/2 particle ina magnetic ï¬eld. If Sx is found to be ¯h/2, what is the probabilityof getting Sz equal to ¯h/2?. What is the probability of getting Syequal to −¯h/2 ? What is the probability of getting Sx equal to−¯h/2
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