# Rotation in QM

#### folgorant

hi all,
I have a problem about rotation operator in QM.
I must verify that $$(\hat{U}(R)f)(\textbf{x})=f(R^{-1}\textbf{x})$$

with: $$\hat{U}(R) = exp({\frac{-i\varphi\textbf{nL}}{\hbar}})$$

R rotation on versor n of angle $$\varphi$$

I don't really know how to start, so please give me an advice!!

#### nrqed

Homework Helper
Gold Member
hi all,
I have a problem about rotation operator in QM.
I must verify that $$(\hat{U}(R)f)(\textbf{x})=f(R^{-1}\textbf{x})$$

with: $$\hat{U}(R) = exp({\frac{-i\varphi\textbf{nL}}{\hbar}})$$

R rotation on versor n of angle $$\varphi$$

I don't really know how to start, so please give me an advice!!
In the exponential, write L as a differential operator. Then expand the exponential to first order.

On the rhs, write explicly the transformed coordinates $$R^{-1} x$$ to first order im the rotation parameters. Next, Taylor expand $$f( R^{-1} x)$$ to first order in those parameters.

The two sides will be equal

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