Assignment 1 - Department of Physics - Carleton University

5. Consider again a particle with orbital angular momentum ℓ = 1 and spin s = 1 in the state
|Ψ〉, which can be expressed in the eigenbasis |mℓ, ms〉 as in problem 4 as
|Ψ〉 = 1
√ 2 |+1, −1〉 + 1
√ 2 |0, 0〉. (4)
(a) If you were to measure Lz in this state, what would be the possible outcomes and their
probabilities?
(b) If you were to measure J 2 in this state, what would be the possible outcomes and their
probabilities?
(c) Now imagine that you make the measurement of J 2 in this state and get the value 6¯h 2 .
What is the new state of the particle after the measurement? Express this new state in
both the |j, mj〉 and the |mℓ, ms〉 eigenbases.
(d) If you were to measure Lz in this new state, what would be the possible outcomes and
their probabilities?