# [Q]Momentum eigenstate normailization

1. Oct 12, 2008

### good_phy

Hi

I use liboff quantum mechanics text book fourth edition.

5.25 fomula of 122 page is $\frac{1}{\sqrt{2\pi}}e^{ikx}$

I thought it is nomalized, but i don't know exactly why $\sqrt{2\pi}$ is denominator.

I think it seemed to be linked Dirac-delta function [itex] \int_{\infty}^{\infty}\frac{1}{2\pi}e^{i(k-k^{'})x} = \delta(k-k^')[/atex] but i have no idea what is going on exactly.

2. Oct 12, 2008

### CompuChip

I think it is because of his definition of Fourier transform. Different people use different conventions. In the end, they are all equivalent of course and should give the same results.

See, for example this link ("Other conventions" section).

3. Oct 12, 2008

### good_phy

Thank you so much that i found Fourier transform is included general innerproduct

in some mathematical space as l Fourier transform is just analogous to vector

innerproduct between momentum eigenfunction and statefunction. thank you.

but i have one questiong. what is hilbert space in which general vectorproduct is

defined?

4. Oct 13, 2008

### George Jones

Staff Emeritus
What do you mean by general vector product?

5. Oct 13, 2008

### good_phy

It means innerproduct such as $$<\varphi_{k}|\varphi{_{k^'}}>$$ i described

product of this form as more general form of 'vector innerproduct in normal vector space'

Last edited: Oct 13, 2008