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Exponential of an operator into bra-ket notation

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data

    The question is to evaluate the expression e^-iA, where A is a Hermitian operator whose eigenvalues are known (but not given) using bra-ket algebra.

    2. Relevant equations

    See above.

    3. The attempt at a solution

    I have been looking around, reading the textbook and course notes, checking the web and so on. I have learned that an expression in this form is a 'unitary operator', and what that means.

    I'm pretty comfortable with the bra-ket notation, but I'm struggling just to *get into it*. ;-)

    If you can help me find a 'way in' to get started, that'd be great: at this point I'm still just kinda staring blankly at it, despite all my efforts so far.

    Oh, yeah, I overhead another student mention using a Taylor series. I get how to convert the exponential to a Taylor series, but I'm not so sure how it helps... and the other student might be wrong.
     
  2. jcsd
  3. Mar 10, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi Bravus! Welcome to PF! :smile:

    (try using the X2 button just above the Reply box :wink:)
    I think they mean if A|xn> = λn |xn>,

    then what is e-iA|∑anxn> ? :smile:
     
  4. Mar 10, 2012 #3
    Thanks for the tip on the nicenesses allowed by the forum software - so nice after spending time answering math and physics questions on 'Yahoo Answers' and having to struggle with all-text!

    Not sure the answer is giving me a way in, though: maybe I'm just thick. The question definitely just says 'evaluate e-iA'.
     
  5. Mar 11, 2012 #4

    tiny-tim

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    Hi Bravus! :smile:

    (just got up :zzz:)

    but anyway, what is e-iA|∑anxn> ? :smile:
     
  6. Mar 11, 2012 #5
    Thanks, and the hint is definitely a handy one. It's Mr Taylor and his Series that really gets the job done in this instance, though...
     
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