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?