Prove the operator d/dx is hermitian

  • Thread starter baldywaldy
  • Start date
  • #1
20
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Hiya :) the title is meant to be prove it isn't hermitian

Homework Statement


Prove the operator d/dx is hermitian


Homework Equations


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


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
 

Answers and Replies

  • #2
ehild
Homework Helper
15,523
1,901
Think of integration by parts.

ehild
 
  • #3
20
0
I know intergration by parts but i just dont understand how to apply in this situation because there are two functions and an operator
 
  • #4
ehild
Homework Helper
15,523
1,901
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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