Prove the operator d/dx is hermitian

[baldywaldy]

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 don't know where to go from here, like i said sorry for the lack of latex usage :(.

Thanks for the help :D

 

[ehild]

Think of integration by parts.

ehild

 

[baldywaldy]

I know intergration by parts but i just don't understand how to apply in this situation because there are two functions and an operator

 

[ehild]

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

You have to show that \int{f_n f&#039;_mdx}\neq (\int{f&#039;_n f_mdx})^*

ehild