6. Consider a qubit used as a clock. The Hamiltonian for the system is H= hw 1)(1, where w is some constant frequency. (a) What are the energy eigenstates and their energies? (b) Write down the time evolution operator U(t) for this system. (c) We prepare the clock in an initial state |(0)) = (10) + |1)). What is the state T(1)) at a later time t?
6. Consider a qubit used as a clock. The Hamiltonian for the system is H= hw 1)(1, where w is some constant frequency. (a) What are the energy eigenstates and their energies? (b) Write down the time evolution operator U(t) for this system. (c) We prepare the clock in an initial state |(0)) = (10) + |1)). What is the state T(1)) at a later time t?
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number 6 a b c please
Transcribed Image Text:6. Consider a qubit used as a clock. The Hamiltonian for the system is H = hw|1)(1|,
where w is some constant frequency.
(a) What are the energy eigenstates and their energies?
(b) Write down the time evolution operator U(t) for this system.
(c) We prepare the clock in an initial state |(0)) = (10) + |1)). What is the state
l(t)) at a later time t?
(d) What is AE for this system?
(e) Let At denote the time it takes for the system to evolve from (0)) to some other
distinguishable state. Calculate AE At and compare your result to the time-energy
uncertainty relation.
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