Rotation in QM

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

with: [tex] \hat{U}(R) = exp({\frac{-i\varphi\textbf{nL}}{\hbar}}) [/tex]

R rotation on versor n of angle [tex]\varphi[/tex]

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

nrqed

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

with: [tex] \hat{U}(R) = exp({\frac{-i\varphi\textbf{nL}}{\hbar}}) [/tex]

R rotation on versor n of angle [tex]\varphi[/tex]

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 [tex] R^{-1} x [/tex] to first order im the rotation parameters. Next, Taylor expand [tex]f( R^{-1} x) [/tex] to first order in those parameters.

The two sides will be equal
 

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