Normalization of a wave function

[Feynmanfan]

Normalization of a wavefunction

Let Phi be a wave function,

Phi(x)= Integral of {exp(ikx) dk} going k from k1 to k2

I'm having trouble normalizing the wave function. I calculated the integral, then multiply by its conjugate and now I'm supposed to integrate again /Phi(x)/^2 in all the space in order to find the normalization constant. I get a non trivial integral so I think it must be easier if I understand the physical meaning of the exercise. I know that exp(ikx) are the eigenfunctions of the mometum operator.

Is it the mathematics I'm doing wrong or is there another way. Thanks for your help.

 

[CarlB]

First, if you want answers in this forum, it is well worth your while to learn LaTex. If a guy who wears a hard hat can do LaTex, then so can you.

From your description of the problem, the "non trivial" integral you're getting is presumably:

$$|\phi|^2 = \int_{-\infty}^\infty \int_{k1}^{k2} \int_{k1}^{k2} e^{-ilx}e^{ikx}dk\; dl\; dx.$$

To solve this integral, do the integration over x first. If this seems impossible, look around for information on "delta functions". The delta function will allow you to do another one of the integrals pretty much trivially, and then the final integral will be easy.

Carl