This problem associated with chapter 7 was assigned during lecture.

Does L̂𝓏 commute with 𝐫̂²?

	[L̂𝓏,𝐫̂²] = L̂𝓏 𝐫̂² - 𝐫̂² L̂𝓏.

	L̂𝓏 𝐫̂² - 𝐫̂² L̂𝓏.

Using the position representations, in spherical coordinates,

	L̂𝓏 ≐ -ιħ∂/∂θ and 𝐫̂² ≐ 𝐫²,

	L̂𝓏 𝐫̂² - 𝐫̂² L̂𝓏 = 𝐫² ιħ∂/∂θ - ιħ∂/∂θ 𝐫².

𝐫² has no θ dependence, so it can be separated from any quantity differentiated with respect to theta, I.E.,

    ∂/∂θ 𝐫² = 𝐫² ∂/∂θ.

    𝐫² ιħ∂/∂θ - ιħ∂/∂θ 𝐫² = 𝐫² ιħ∂/∂θ -  𝐫² ιħ∂/∂θ = 0 = [L̂𝓏,𝐫̂²] = 0.

    [L̂𝓏,𝐫̂²] = 0, so these quantities commute.