# Prove the operator d/dx is hermitian

1. Oct 20, 2011

### baldywaldy

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. Oct 20, 2011

### ehild

Think of integration by parts.

ehild

3. Oct 20, 2011

### baldywaldy

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. Oct 20, 2011

### ehild

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

You have to show that

$\int{f_n f'_mdx}\neq (\int{f'_n f_mdx})^*$

ehild