Schaum's Quantum Mechanics comes up with
$$\exp((-i/\hbar)\cdot \theta \cdot{\hat{L}} \cdot {\overrightarrow{n}})$$
as the formula of the rotation operator. Other sources I see don't have the negative sign. How did they get the negative sign in here?
Answer
Both negative sign and positive sign are correct. When you make an infinitesimal rotation with angle $d\phi$ about the z-axis, then both two following representations for transformed coordinates are true: $$ \left\{ \begin{array}{ll} x'=x-d\phi y \\ y'=y+d\phi x \end{array} \right. $$ and $$ \left\{ \begin{array}{ll} x'=x+d\phi y \\ y'=y-d\phi x \end{array} \right. $$ The former leads to the positive sign, while the later leads to the negative sign.
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