Jump to content

Recommended Posts

Posted (edited)

How was the equation highlighted in the attachment below simplified. I get the other term but another highlighted term went to zero, how?


The hand writing is where I tried using integration by parts. 

A’ = ih/2m



Edited by Lizwi

Share this post

Link to post
Share on other sites

It is because you are evaluating the integral at the limits of integration. That's very common in any field theory. The fields are assumed to go to zero fast enough at infinity.

In fact, you need that if you want your momentum operator to be Hermitian. If D is any of these differential operators, you need both the i and the vanishing at infinity so that,

\[\int d^{3}xF^{*}iD\left(G\right)=\int d^{3}x-\left(DF^{*}\right)iG=\]

\[=\int d^{3}x\left(iDF\right)^{*}iG\]

I hope that helps.

Good question. +1 :D

Share this post

Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.