The text just says that a \left(k\right) is real. So its derivative is also real. But the derivative is multiplied by i making it purely imaginary. So some how when these are multiplied and then integrated the integral is zero which I don't understand. Let me know if more clarification is...
So I'm reviewing some mathematics for quantum mechanics and this came equation came up
\int_{-\infty}^{\infty} a \left( k \right)^{*} i \dfrac{d\,a\left(k\right)}{dk}dk.
If a \left( k \right) is constrained to be real then this integral is zero or so the text says. Why is this the case...
I don't know much about quantum linear response theory but I am also trying to learn. I found a series of lecture notes by Andrei Tokmakof at MIT. This one seems to be the most relevant.
http://www.mit.edu/~tokmakof/TDQMS/Notes/8._Linear_Response_2-09.pdf.
I'm not sure if this belongs here or in the physics section. The mathematical definition of curvature is the derivative of the unit tangent vector normalized to the arc length: \kappa = \frac{dT}{ds}. If we apply this to a parabola with equation y = x^{2} we get \frac{2}{(1+4x^{2})^{3/2}}...