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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

080DEC72-A152-4CD0-A5C2-1958461B177C.jpeg

A50BE6EC-C4FE-440D-8BE4-C3EA07369D3F.jpeg

Edited by Lizwi

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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

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