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I am trying to calculate L^2 in spherical coordinates. L^2 is the square of L, the angular momentum operator. I know L in spherical coordinates. This L in spherical coordinates has only 2 components : one in the direction of the theta unit vector and one in the direction of the phi unit vector.

I get the correct result for L^2 by substituting cartesian values for the theta and phi unit vectors in L, and then squaring and adding the components.

I do not get the correct result by simply squaring and adding the theta and phi components of L directly.Why not? Surely if this were a classical vector whose components are scalars rather than operators, I could find its norm squared in both ways, isn't it?

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# L^2 in spherical coordinates.

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