Table of Contents

# QM States for Rigid Rotor

## Prerequisites

Students should be able to:

## In-class Content

- Combinations of $Y_{l,m}(\theta,\phi)$ and the Spherical Harmonic Series (Lecture, 25 minutes)
- Finding the Coefficients of a Spherical Harmonic Series (Small Group Activity, 25 minutes)
- Plotting Linear Combinations of Spherical Harmonics (Maple Activity, 15 minutes)

## Homework for Central Forces

- (AngMomProb)
An angular momentum system with $l=1$ is prepared in the state: $$\ket{\psi}=\frac{2}{\sqrt{29}}\ket{1,1}+i\frac{3}{\sqrt{29}}\ket{1,0}-\frac{4}{\sqrt{29}}\ket{1,-1}$$

What are the possible results of a measurement of the angular momentum component $L_z$, and with what probabilities would they occur?

What are the possible results of a measurement of the angular momentum component $L_x$, and with what probabilities would they occur?

Plot histograms of the predicted measurement results from parts (a) and (b).