Quantum Mechanics | Part IB, 2004

A quantum mechanical system is described by vectors ψ=(ab)\psi=\left(\begin{array}{l}a \\ b\end{array}\right). The energy eigenvectors are

ψ0=(cosθsinθ),ψ1=(sinθcosθ)\psi_{0}=\left(\begin{array}{c} \cos \theta \\ \sin \theta \end{array}\right), \quad \psi_{1}=\left(\begin{array}{c} -\sin \theta \\ \cos \theta \end{array}\right)

with energies E0,E1E_{0}, E_{1} respectively. The system is in the state (10)\left(\begin{array}{l}1 \\ 0\end{array}\right) at time t=0t=0. What is the probability of finding it in the state (01)\left(\begin{array}{l}0 \\ 1\end{array}\right) at a later time t?t ?

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