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!

Using the Baker-Campbell-Hausdorff Identity

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Given that U = e[itex]^{-i*θ*\hat{n}*\vec{J}/hbar}[/itex]

    Show that U[itex]^{†}[/itex][itex]\vec{J}[/itex]U = [itex]\hat{n}(\hat{n}*\vec{J}) - \hat{n}\times(\hat{n}\times\vec{J})cos(θ) + \hat{n}\times\vec{J}sin(θ)[/itex]

    2. Relevant equations
    The Baker-Campbell-Hausdorff Identity


    3. The attempt at a solution
    U[itex]^{†}[/itex][itex]\vec{J}[/itex]U = e[itex]^{-i*θ*\hat{n}*\vec{J}/hbar}[/itex][itex]\vec{J}[/itex]e[itex]^{i*θ*\hat{n}*\vec{J}/h_bar}[/itex]

    U[itex]^{†}[/itex][itex]\vec{J}[/itex]U = [itex]\vec{J} + [i*θ*\hat{n}*\vec{J}/hbar,\vec{J}]+[i*θ*\hat{n}*\vec{J}/hbar,[i*θ*\hat{n}*\vec{J}/hbar,\vec{J}]]/2! + ...[/itex]

    I guess I just need some help on whether or not I am headed in the right direction.
     
    Last edited: Feb 29, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Using the Baker-Campbell-Hausdorff Identity
Loading...