(4) Consider a system described by the Hamiltonian H, H = 0 a a 0 !,...

(4) Consider a system described by the Hamiltonian H, H = 0 a a 0 !,
where a is a constant. (a) At t = 0, we measure the energy of the system, what possible values will we obtain? (b) At later time t, we measure the energy again, how is it related to its value we obtain at t = 0 ? (c) If at t = 0, the system is equally likely to be in its two possible states, write down the most general state of the 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 in a magnetic ﬁeld. If Sx is found to be ¯h/2, what is the probability of getting Sz equal to ¯h/2?. What is the probability of getting Sy equal to −¯h/2 ? What is the probability of getting Sx equal to −¯h/2
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genius_generous answered 1 year ago

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