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d3nat
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Homework Statement
Solve for ##L^2_x##
##L_x = \frac{\hbar}{i} (-sin(\phi)\frac{d}{d\theta} - cos(\phi)cot(\theta)\frac{d}{d\phi}##** the d's should be partial derivatives, but I'm not sure how to do that symbol. Sorry!
Homework Equations
Solve for ##L^2_x##
##L_x = \frac{\hbar}{i} (-sin(\phi)\frac{d}{d\theta} - cos(\phi)cot(\theta)\frac{d}{d\phi}##** the d's should be partial derivatives, but I'm not sure how to do that symbol. Sorry!
The Attempt at a Solution
I'm trying to square everything
But can I square partial derivatives? Is that the same thing as a second derivative?
so ##-\hbar^2 \Big( sin^2(\phi)\frac{d^2}{d^2\theta} + cos^2(\phi)cot^2(\theta)\frac{d^2}{d^2\phi} +sin(\phi)\frac{d}{d\theta}(cos(\phi)cot(\theta)\frac{d}{d\phi}) +cos(\phi)cot(\theta)\frac{d}{d\phi}(sin(\phi)\frac{d}{d\theta}) \Big)##
Can I take a partial derivative of a partial derivative?
I'm so stumped. Can't seem to find any explanations online. Help please?
[EDIT:]
Is this the simplest form?
##-\hbar^2 \Big( sin^2(\phi)\frac{d^2}{d^2\theta} + cos^2(\phi)cot^2(\theta)\frac{d^2}{d^2\phi} -sin^2(\phi)cos(\phi)cot(\theta)\frac{d}{d\phi}+cos^2(phi)cot(\theta)\frac{d}{d\theta}##
I still don't think this is right.
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