1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Unitary operator U ?

  1. Jan 30, 2012 #1

    I have to show that a unitary operator [itex] U [/itex] can be written as


    where [itex] K [/itex] is a Hermitian operator.

    Now how could you possibly have a fraction of operators if those can be represented by matrices? Not sure what to do here.
  2. jcsd
  3. Jan 30, 2012 #2
    Also doesn't the equality fail for when U=-1 (the negative of a 1 matrix)? No matter what K is I can't see how it would hold since we'd basically end up with -1 + iK = 1 + iK
  4. Jan 30, 2012 #3
    Hi erogard,

    First think about what an Unitary operator is by definition.

    with just a quick look at wikipedia you'll be able to see that
    U^{*}U = UU^* = I
    so given that K is hermitian
    and that
    I^*I = II^*=I
    just see if the above identity holds,

  5. Jan 30, 2012 #4
    Stuff written like that generally just means inverse eg

    So you just want to show that U us unitary eg [itex]UU^{\dagger}=U^{\dagger}U=I[/itex] (where[itex]\dagger[/itex] is the hermitian conjugate operation)
    Which is a pretty simple operation
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook