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Extra problem: The basis of the l = 1 Hilbert space in the (L2, Lz) representation are Y11(θ,...

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Physics

Extra problem: Thebasis of the l = 1 Hilbert space in the(L2, Lz) representation areY11(θ, φ),Y10(θ, φ),Y1-1(θ, φ).

(1) Find the matrixexpressions of Lx, Ly andLz. Hint: make use of L+and L-.

(2) Suppose the systemis in a normalized state Ψ =c1Y11+c2Y10. Find the possiblevalues and corresponding possibilities when measuringLz, L2, andLx, respectively.

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