Student handout: Hydrogen Probabilities in Matrix Notation

Central Forces 2022
This activity reinforces the strategies students have been practicing on each system by letting them create their own matrix operators and columns on the hydrogen atom and do some calculations with them.
What students learn
  • How to index through \(n\), \(\ell\), and \(m\) in the matrix representation.
  • A refresher on doing calculations like finding probabilities and expectation values in matrix representation.

For the state \[ \left|{\Psi}\right\rangle = \sqrt{\frac{7}{10}} |2, 1, 0\rangle + \sqrt{\frac{1}{10}} |3, 2, 1\rangle + i\sqrt{\frac{2}{10}} |3, 1, 1\rangle\]

  1. Convert the state to matrix notation.
  2. Find \(\mathcal{P}(L_z=0\hbar)\)
  3. Find \(\langle E\rangle\)


Keywords
Matrix Hyrdogen Hydrogen Atom Probabilities Expectation Values
Learning Outcomes