4**. A quantum system has a time-independent Hamiltonian H and at a given time, t = 0, it is in the state V=> akk k=1 where, for all 1 ≤ k ≤d, Þ is an eigenstate of H with eigenvalue X- a) Show that the temporal evolution of the state is as follows: (t) = [et Σ k=1 takk b) Is the previous expression for y(t) valid for negative times? that is, is it valid for the past?
4**. A quantum system has a time-independent Hamiltonian H and at a given time, t = 0, it is in the state V=> akk k=1 where, for all 1 ≤ k ≤d, Þ is an eigenstate of H with eigenvalue X- a) Show that the temporal evolution of the state is as follows: (t) = [et Σ k=1 takk b) Is the previous expression for y(t) valid for negative times? that is, is it valid for the past?
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Transcribed Image Text:4**. A quantum system has a time-independent Hamiltonian H and at a given time, t = 0, it is in
the state
V=> akk
k=1
where, for all 1 ≤ k ≤d, Þ is an eigenstate of H with eigenvalue X-
a) Show that the temporal evolution of the state is as follows:
(t) = [et
Σ
k=1
takk
b) Is the previous expression for y(t) valid for negative times? that is, is it valid for the past?
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