Quantum Fundamentals 2022
Consider a two-state quantum system with a Hamiltonian
\begin{equation}
\hat{H}\doteq
\begin{pmatrix}
E_1&0\\ 0&E_2
\end{pmatrix}
\end{equation}
Another physical observable \(M\) is described by the operator
\begin{equation}
\hat{M}\doteq
\begin{pmatrix}
0&c\\ c&0
\end{pmatrix}
\end{equation}
where \(c\) is real and positive. Let the initial state of the system be \(\left|{\psi(0)}\right\rangle
=\left|{m_1}\right\rangle \), where \(\left|{m_1}\right\rangle \) is the eigenstate corresponding to the larger of the two possible eigenvalues of \(\hat{M}\). What is the expectation value of \(M\) as a function of time? What is the frequency of oscillation of the expectation value of \(M\)?