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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
    <m|x|n>
    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
    <m|n>=[tex]\delta[/tex]mn

    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
    [tex]x=.5*\sqrt{2h/mw}(A+A^{+})[/tex]?
    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
     
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