Extra problem: The basis of the l = 1 Hilbert space in the (L2, Lz) representation...

Extra problem: The basis of the l = 1 Hilbert space in the (L², L_z) representation are Y₁₁(θ, φ), Y₁₀(θ, φ), Y_1-1(θ, φ).

(1) Find the matrix expressions of L_x, L_y and L_z. 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 L_z, L², and L_x, respectively.

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genius_generous answered 1 year ago

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