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I am trying to learn about some basic quantum mechanics.

http://farside.ph.utexas.edu/teaching/qmech/lectures/node35.html this website shows that the time derivative of the momentum expectation d<p>/dt = -<dV/dx>

The part that i am not getting is how the writer goes from the first line of equation 157 on the site, to the second line of the same equation. He simply says he is integrating by parts.

I've tried integrating the 2 terms of the integrand in the first line by parts, but I am not really getting to the second line. I assume that integrating the 2 terms independently should give u1v1 - u2v2 = 0 so that we are left only with the integrals of v1du1 and v2du2(this is judging by the fact that the second line is entirely an integral).

Can someone clear up this step?

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# Time derivative of momentum expectation?

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