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What's the difference between them

  1. Feb 27, 2008 #1
    <n|m> ;


    |m><n| ;
     
  2. jcsd
  3. Feb 27, 2008 #2

    pam

    User Avatar

    <n|m> is a number.
    |m><n| is an operator that would act on one wave function to give a different one.
     
  4. Feb 27, 2008 #3
    appreciate it!

    i know the product.
    but what the operator is?
    is it pesi(m)pesi(n)*?
     
  5. Feb 27, 2008 #4
    do you mean :
    when it act on one wave function,it denotes
    |m><n|a> ?
     
  6. Feb 27, 2008 #5
    Think of it as *all* 1xN matrices
    [tex]
    |n>=A=\begin{pmatrix}
    a\\b\\c\\\ldots
    \end{pmatrix}
    [/tex]
    [tex]
    <n|=A^\dag=\begin{pmatrix}
    a^* & b^* & c^* & \ldots
    \end{pmatrix}
    [/tex]
    [tex]
    \psi_n(x)=<x|n>
    [/tex]
    Then you see that [itex]|m><n|[/itex] is a matrix ("sort of operator"). [itex]<m|n>[/itex] is a number (like the vector scalar product). Note that [itex]<n|m>\neq \psi_n^*(x)\psi_m(x)[/itex], however since [itex]\sum_x |x><x|=1[/itex]
    [tex]<n|m>=\sum_x <n|x><x|m>=\sum_x \psi_n^*(x)\psi_m(x)[/tex]
    So
    1. don't rearrange |n> expressions
    2. only numbers <n|m> commute
    3. if you ever get to <x|n>, you can substitute with [itex]\psi_n(x)[/itex]
     
  7. Feb 27, 2008 #6

    clem

    User Avatar
    Science Advisor

    Yes.........
     
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