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In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!

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Rotating a wavefunction to get an exponential of $L^2$ and $L_z$

that the question is not about finding an expression for the general rotation but about finding any rotation that can be expressed as an exponential that includes $L^2$ and possibly $L_z$ but no other operators
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Identity in quantum operator tutorial

I'm reading this tutorial by Ben Simons entitled Operator methods in quantum mechanics in connection with his course in advanced QM, and I'm a bit puzzled by an identity in page 25, a bit above relati …
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