Quantum Mechanics Solution Manual 

© Leon van Dommelen 

4.4.2.2 Solution esdbb
Question:
Continuing the previous question, what are the standard deviations in energy, square angular momentum, and angular momentum?
Answer:
Since the expectation value in energy is , as are the eigenvalues of each state, the standard deviation is zero.
This is expected since every measurement produces ; there is no deviation from that value.
Similarly the standard deviation in is zero:
For the angular momentum, the expectation value is zero but the two states have eigenvalues and , so
Whether or is measured, the deviation from zero has magnitude .