Solution to 1986 Problem 56

Let \psi_j be the eigenfunctions of the operator Q. Let q_j be the eigenvalue associated with \psi_j. Expand \psi in terms of the eigenstates \psi_j of Q
\begin{align*}\psi = \sum_{j = 0}^{\infty} c_j \psi_j\end{align*}
\begin{align*}\psi^* = \sum_{j = 0}^{\infty} c_j^{*} \psi_j^*\end{align*}
\begin{align*}\int \psi^* Q \psi = \sum_{j = 0}^{\infty} \left|c_j \right|^2 q_j\end{align*}
which is the expectation value of the physical observable that Q represents. Therefore, answer (C) is correct.

return to the 1986 problem list

return to homepage

Please send questions or comments to where X = physgre.