1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rotation in QM

  1. Mar 31, 2008 #1
    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!!
     
  2. jcsd
  3. Mar 31, 2008 #2

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?