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: Quesion on dirac notation

  1. Nov 1, 2008 #1
    I have recently finished reading a section on this notation, and while i though i understood it, i now find myself lost

    The question is to show that
    Is zero unless m = n + or - 1

    As I understand it so far <m| and |n> correspond to the eigenstates of an arbitrary system and x is just supposed to be the x operator

    The only thing i could think to do with his was plug into
    [tex]\int[/tex]m*xn dx but that did not help me

    I also susspect i need to use that

    If anyone could give me a nudge in the correct direction it would be much appreciated.
  2. jcsd
  3. Nov 1, 2008 #2
    This question is meant to be about the energy eigenstates of the harmonic oscillator, not an arbitrary system.
  4. Nov 2, 2008 #3
    I'm sry, but I still do not really understand where to go with this, I suppose I can use |n> = the nth eigenstate of the harmonic oscillator, but isn't the x operator just x?
  5. Nov 2, 2008 #4
    Haven't you seen the "ladder operators" a^+ and a^-?
  6. Nov 2, 2008 #5
    I have, and if x were a ladder operator this would be trivial, but I thought it was supposed to be the x (position) operator....
  7. Nov 2, 2008 #6
    You can write the x operator in terms of the ladder operators. Your question is trivial, too.
  8. Nov 2, 2008 #7
    So then would i write
    and distribute out getting
    (<m|A|n>+<m|A^+|n>) * some constant
  9. Nov 2, 2008 #8
    Indeed! And all you need is to show for what m,n combinations <m|A|n>+<m|A^+|n> is nonzero, which as you said is trivial.
  10. Nov 2, 2008 #9
    It makes sense now, thank you for your help
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook