# Quesion on dirac notation

I have recently finished reading a section on this notation, and while i though i understood it, i now find myself lost

The question is to show that
<m|x|n>
Is zero unless m = n + or - 1

As I understand it so far <m| and |n> correspond to the eigenstates of an arbitrary system and x is just supposed to be the x operator

The only thing i could think to do with his was plug into
$$\int$$m*xn dx but that did not help me

I also susspect i need to use that
<m|n>=$$\delta$$mn

If anyone could give me a nudge in the correct direction it would be much appreciated.

This question is meant to be about the energy eigenstates of the harmonic oscillator, not an arbitrary system.

I'm sry, but I still do not really understand where to go with this, I suppose I can use |n> = the nth eigenstate of the harmonic oscillator, but isn't the x operator just x?

Haven't you seen the "ladder operators" a^+ and a^-?

Haven't you seen the "ladder operators" a^+ and a^-?

I have, and if x were a ladder operator this would be trivial, but I thought it was supposed to be the x (position) operator....

You can write the x operator in terms of the ladder operators. Your question is trivial, too.

So then would i write
$$x=.5*\sqrt{2h/mw}(A+A^{+})$$?
and distribute out getting
(<m|A|n>+<m|A^+|n>) * some constant

So then would i write
$$x=.5*\sqrt{2h/mw}(A+A^{+})$$?
and distribute out getting
(<m|A|n>+<m|A^+|n>) * some constant

Indeed! And all you need is to show for what m,n combinations <m|A|n>+<m|A^+|n> is nonzero, which as you said is trivial.

It makes sense now, thank you for your help