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