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

What's the difference between them

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

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


    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
    a^* & b^* & c^* & \ldots
    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]
    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


    User Avatar
    Science Advisor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook