\(\newcommand{\ket}[1]{\vert#1\rangle}\)
Consider the state \(\ket{\psi}\) given by \(\begin{equation*} \ket{\psi} = c_1
\ket{E_1} + c_2 \ket{E_2}. \end{equation*} \)Answer the following questions.
- Give condition(s) on \(E_1, E_2\) so that \(\ket{\psi}\) may be a stationary state for arbitrary \(c_1, c_2\).Can the state represented by \(\ket{\psi}\) be a stationary state when \(E_1\ne E_2\)? If yes, give condition(s) on \(c_1,c_2\).
- Let \(E_1, E_2, c_1, c_2\) be such that \(\ket{\psi}\) is {\bf not} a stationary state. Compute the probability that a measurement of energy gives a value\(E_1\) at time \(t\). Does the probability vary time. WHY?
- Let \(E_1, E_2, c_1, c_2\) be as in part \ref{IT3}. Now under what conditions that a dynamical variable \(X\) must obey so that the average of \(X\) remains constant?
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4727:Diamond Point
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