In: Physics
Extra problem: The basis of the l = 1 Hilbert space in the (L2, Lz) representation are Y11(θ, φ), Y10(θ, φ), Y1-1(θ, φ).
(1) Find the matrix expressions of Lx, Ly and Lz. Hint: make use of L+ and L-.
(2) Suppose the system is in a normalized state Ψ = c1Y11 +c2Y10. Find the possible values and corresponding possibilities when measuring Lz, L2, and Lx, respectively.