Central Forces 2022
- How to translate a complicated wavefunction into eigenstates.
- Refresher on how to find expectation values and probabilities in a region.
- How to use the symmetry of the wavefunction to tell you something about measurements.
What students learn
- How to translate a complicated wavefunction into eigenstates.
- Refresher on how to find expectation values and probabilities in a region.
- How to use the symmetry of the wavefunction to tell you something about measurements.
Consider the following normalized quantum state on a unit ring:
\begin{equation}
\Phi(\phi)=\sqrt\frac{8}{3 \pi r_0} \sin^{2}\left( 3\,\phi \right)\cos \left( \phi \right)
\end{equation}
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Express this state in the \(L_z\) basis, using three representations: wavefunction, bra/ket, and matrix representations. Remember that you can use any of these representations in the following calculations.
What is the expectation value of \(L_z\) in this state?
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What is the probability that the particle can be found in the region \(0<\phi<
\frac{\pi}{4}\)? Repeat your calculation in the region \(\frac{\pi}{4}<\phi< \frac{3 \pi}{4}\)?
- Keywords
- probability angular momentum probability in a region continuous wavefunction representations
- Learning Outcomes
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