# Quantum Calculations on the Hydrogen Atom

Keywords: Central Forces, Quantum Mechanics, Hydrogen Atom, Eigenstates, Hermitian Operators, Angular Momentum, Quantum Measurements, Degeneracy, Eigenvalues, Small Group Activity

### Highlights of the activity

1. This small group activity is designed to help students practice measuring properties of the Hydrogen atom.
2. Students work in small groups to find the matrices that correspond to $H$, $L^2$, and $L_z$ operators, and how they operate on the states of the Hydrogen atom, $|n,\ell,m\rangle$.
3. The whole class wrap-up discussion includes group presentations, allowing students to observe a variety of useful techniques when solving for the properties of a state of hydrogen.

### Reasons to spend class time on the activity

This activity gives students the chance to see that all of same calculations that they did for the ring and the sphere apply to the Hydrogen atom. This is also an excellent opportunity to re-emphasize the affordances of different representations, how to deal with degeneracy, and what the conditions are for time dependence.

### Instructor's Guide

Authors: Corinne Manogue, Mary Bridget Kustusch, David McIntyre

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