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Prove the operator d/dx is hermitian

  1. Oct 20, 2011 #1
    Hiya :) the title is meant to be prove it isn't hermitian

    1. The problem statement, all variables and given/known data
    Prove the operator d/dx is hermitian


    2. Relevant equations
    I know that an operator is hermitian if it satisfies the equation : <m|Ω|n> = <n|Ω|m>*


    3. The attempt at a solution
    Forgive the lack of latex , I have know idea how to use it and find it baffling.

    the intergral of (fm* d/dx fn) dx = the intergral of fm* d fn
    ={fm* fn - the intergral of fn d fm*} between the limits x=infinity and - infinity.

    This is where i get stuck. I just dont know where to go from here, like i said sorry for the lack of latex usage :(.

    Thanks for the help :D
     
  2. jcsd
  3. Oct 20, 2011 #2

    ehild

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    Think of integration by parts.

    ehild
     
  4. Oct 20, 2011 #3
    I know intergration by parts but i just dont understand how to apply in this situation because there are two functions and an operator
     
  5. Oct 20, 2011 #4

    ehild

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    d/dx f means that you differentiate f with respect to x. d/dx f = df/dx = f'

    You have to show that


    [itex]\int{f_n f'_mdx}\neq (\int{f'_n f_mdx})^*[/itex]

    ehild
     
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