Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Creation and Annihilation Operators

  1. Dec 9, 2012 #1
    We know that

    a|n> = √n | √(n-1)>


    a' |n> = √(n+1) | n + 1 >

    so, If we use this to find


    it would be equal to n

    <n|a'a|n> = n

    Am I correct?

    I'm not really sure about my calculations.

    I operate with a first so.

    <n|a' √n | √(n-1)>

    = n


    Can someone please help me with the complete solution?
  2. jcsd
  3. Dec 9, 2012 #2


    User Avatar
    2017 Award

    Staff: Mentor

    <n|a'a|n> = <n|a' √n | (n-1)> (no square root for the state)
    = √n <n|a' | (n-1)> (√n is a scalar, you can pull it out)
    = √n <n|√n | n>
    = √n √n <n|n>
  4. Dec 9, 2012 #3
    Thanks :)) yah no √ for the state. Sorry.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook