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Calculating Expectation Values in Superposition States
The Prompt
$$\vert\Phi\rangle=\frac{1}{\sqrt{5}}\vert\varphi_1\rangle+\sqrt{\frac{3}{5}}\vert\varphi_2\rangle+\frac{1}{\sqrt{5}}\vert\varphi_3\rangle$$
Is this superposition of energy eigenfunctions itself an eigenfunction of the Hamiltonian?
Calculate the average value of $x$.
Calculate $\langle H^2 \rangle$
What is the time dependence of the state vector?
the slides need some editing; also too many ideas here for 1 exercise.
Context
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