Physical Chemistry 2 Quiz
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QUANTUM FOUNDATIONS
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A quantum system is described by the Hamiltonian H^=ℏω(∣1⟩⟨1∣+2∣2⟩⟨2∣+∣1⟩⟨2∣+∣2⟩⟨1∣)\hat{H} = \hbar\omega(|1\rangle\langle1| + 2|2\rangle\langle2| + |1\rangle\langle2| + |2\rangle\langle1|) where ∣1⟩|1\rangle and ∣2⟩|2\rangle are orthonormal basis states. If the system is initially prepared in the state ∣ψ(0)⟩=12(∣1⟩+i∣2⟩)|\psi(0)\rangle = \frac{1}{\sqrt{2}}(|1\rangle + i|2\rangle), what is the probability of finding the system in the state ∣ϕ⟩=12(∣1⟩−∣2⟩)|\phi\rangle = \frac{1}{\sqrt{2}}(|1\rangle - |2\rangle) at time t=π2ωt = \frac{\pi}{2\omega}?
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