I Wave packet integral question

1. Nov 7, 2016

knockout_artist

Hi,

what kind if integration used on equation 1 so it turned into equation 2? this does not look like integration by parts. and where (x-x0) appeared from instead of (k-k0) ?

2. Nov 7, 2016

Staff: Mentor

No integration was done. For instance, for the imaginary term, you multiply by the right-hand side by $\exp[i k_0(x-x_0)] \exp[-i k_0(x-x_0)]$, and move the second exponential inside the integral sign.

3. Nov 7, 2016

andrewkirk

No integration has been done yet. It's the old mathematical trick of multiplying and dividing by the same thing.
Outside the integral is a factor of
$$\exp\left[-\frac{(x-x_0)^2}2(\Delta k)^2\right]$$
and inside the integral is a factor of the reciprocal
$$\exp\left[\frac{(x-x_0)^2}2(\Delta k)^2\right]$$
These cancel each other out.

They can be freely moved through the integral sign because they do not involve the integration variable $k$.

EDIT: Darn, Dr Claude jinxed me. Now I'm not allowed to talk for the rest of the day.

4. Nov 7, 2016

dextercioby

I bet you are reading from a Russian book translated into English decades ago.

5. Nov 8, 2016

knockout_artist

:D I have many of those books too.
But this image is from David Bohm's Quantum Theory.