Quantum Mechanics Solution Manual 

© Leon van Dommelen 

4.4.2.1 Solution esdba
Question:
The 2p pointer state of the hydrogen atom was defined as
What are the expectation values of energy, square angular momentum, and angular momentum for this state?
Answer:
Note that the square coefficients of the eigenfunctions and are each , so each has a probability in the 2p state.
Eigenfunction has an energy eigenvalue , and so does , so the expectation value of energy in the 2p state is
This is as expected since the only value that can be measured in this state is .
Similarly, eigenfunction has a square angular momentum eigenvalue , and so does , so the expectation value of square angular momentum in the 2p state is that value,
Eigenfunction has a angular momentum eigenvalue , and has , so the expectation value of angular momentum in the 2p state is
Measurements in which the angular momentum is found to be average out against those where it is found to be .