Quantum Angular Momentum

Question:
An l = 1 particle is in the state,

Use the matrix representation:

a) What are the probabilities that a measurement of Ĺz will yield the value ħ, 0, −ħ for this state?
What is the average value of

b) Use matrix mechanics to evaluate the expectation value of

c) What is the probability that a measurement of Ĺx will yield the value ħ for this state?

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