Trying to see how these are equivalent

[hideelo]

I am working on the derivation of the angular momentum squared operator (in quantum mech.) and there is one step that I don't see how it works. I'm not sure that this is the right place to post it, but since this is a strictly mathematical question, I figured I would post it here. The equivalence is as follows:

(cotθ)(∂/∂θ) + (∂/∂θ)² = (cscθ)(∂/∂θ)[(sinθ)(∂/∂θ)]

I don't see how to go from one to the other

 

[Mark44]

I am working on the derivation of the angular momentum squared operator (in quantum mech.) and there is one step that I don't see how it works. I'm not sure that this is the right place to post it, but since this is a strictly mathematical question, I figured I would post it here. The equivalence is as follows:

(cotθ)(∂/∂θ) + (∂/∂θ)² = (cscθ)(∂/∂θ)[(sinθ)(∂/∂θ)]

I don't see how to go from one to the other

Start on the right side, and take the derivative of (sinθ * (∂/∂θ)), using the product rule. This simplifies to what you have on the left side without too much effort.

 

[hideelo]

Thanks :-) I don't know why I didnt try that