Can the Lippmann-Schwinger equation be integrated over negative r values?

[Manojg]

Hi,

I have a simple question.
I am looking at Sakurai's "Modern Quantum Physics, Revised edition" on page 382 where he tries to integrate the Lippmann-Schwinger equation. From equation 7.1.15 to 7.1.16, he converted from Cartesian to spherical coordinate system. After integration over \phi and cos\theta, he changed the integration over "q" (which is radius in spherical system) from "0 to +infinity" to "-infinity to +infinity".

One can't change radius from -infinity to +infinity in spherical coordinate, right? Then, how did he get that equation?

Thanks.

 

[Bill_K]

I don't have the book, but sure you can do that if the integrand is even. Doesn't mean there is anything physical about negative r, it's just a formal way of evaluating the integral. Maybe what comes next is a contour integration in the complex r plane?