Writing M(x,x') in Dirac Notation: A Guide

[raj2004]

Hey guys,
I am having difficulty interpreting M(x,x') into dirac notation. How do i write M(x,x') in dirac notation? The actual problem is to write the following in dirac notation:

int { int { m(x)* M(x,x') g(x') } dx} dx'

I would appreciate your help.

 

[raj2004]

Homework Statement

Hey guys,
I am having difficulty interpreting M(x,x') into dirac notation. How do i write M(x,x') in dirac notation? The actual problem is to write the following in dirac notation:
I would appreciate your help.

Homework Equations

int { int { m(x)* M(x,x') g(x') } dx} dx'

The Attempt at a Solution

i tried to use M(x,x') = m(x) m(x'). would that be appropriate?

 

[raj2004]

could anyone help me on this ?

 

[mjsd]

what is what in

int { int { m(x)* M(x,x') g(x') } dx} dx'

?

 

[raj2004]

int means integration

 

[mjsd]

and what about m , M, g? are the states, operators .. what is what?

 

[CompuChip]

Consider the inner product $\langle m | M | g \rangle$ and write it out in the position basis (hint, insert the completeness relation twice, once at each vertical bar).

 

[CompuChip]

For your attempt at solution, I don't know what M and m are supposed to be, but if they are what I think they are (M is some sort of propagator and m is a state) then I don't think you can write this.

 

[raj2004]

I think m(x) = <x|M> and m(x)* = <M|x>. But i don't know what to write for M(x,x') in dirac notation. Here x and x' are two different bases. Also, g(x') = <x'|g>.

 

[CompuChip]

Consider the inner product $\langle m | M | g \rangle$ and write it out in the position basis (hint, insert the completeness relation twice, once at each vertical bar).

Have you tried that already?

 

[raj2004]

Ok, now i tried it. Following what you said, I found above integral equals to <m|M|g>. But i don't understand what you mean by M(x,x') is propagator? In dirac notation does M(x,x') equal to <x|M|x'> . It works out fine if i make that assumption.

 

[malawi_glenn]

What does your original integral equal? And what do you mean by "I think m(x) = <x|M> .. " ? You don't know?

 

[raj2004]

No. I was not sure about that statement. But now it's clear. m(x) = <x|m> , not <x|M>. Thanks for your help guys. I get the answer <m|M|g>. But i still don't understand why M(x,x') = <x|M|x'>?

 

[CompuChip]

OK, let me put it this way: do you know what $\int \mathrm{d}x |x\rangle\langle x|$ is?