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Suppose I have a vector operator which angle dependence is given by $\hat O(\theta)=A\sin\theta+B\cos\theta+C$ What can I say about $\hat O$? Sorry, I do realize that it is a bit vague. Assume $\hat O$ is an operator on the space of wavefunctions.


I can see that it is periodic with period $2\pi$, but what else?

Thank you.

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    It is infinitely many times differentiable, satisfying a differential equation $y'+y'''=0$ and $y' = y^{(5)}$.2012-12-11

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