Central Forces 2021
A hydrogen atom is initially in the superposition state
\begin{equation}
\left|{\psi(0)}\right\rangle =\frac{1}{\sqrt{14}}\left|{2,1,1}\right\rangle
-\frac{2}{\sqrt{14}}\left|{3,2,-1}\right\rangle
+\frac{3i}{\sqrt{14}}\left|{4,2,2}\right\rangle .
\end{equation}
What are the possible results of a measurement of the energy and with what
probabilities would they occur? Plot a histogram of the measurement results.
Calculate the expectation value of the energy.
What are the possible results of a measurement of the angular momentum
operator \(\mathbf{L}^2\) and with what probabilities would they occur? Plot a
histogram of the measurement results. Calculate the expectation value of
\(\mathbf{L}^2\).
What are the possible results of a measurement of the angular momentum
component operator \(L_z\) and with what probabilities would they occur? Plot a
histogram of the measurement results. Calculate the expectation value of
\(L_z\).
How do the answers to (a), (b), and (c) depend upon time?