(I'm an independent learner, so no professor to ask.) There is a short example given in a youtube video not in given in any textbooks that I don't really follow. Yet it seems very useful, and possibly like what I want to use to solve a current problem... So I'm trying to understand, not get an exact answer for an exact problem from anyone.
The idea is to solve an exponent for the root or the amount that minimizes the function. Then integrate using the information found from solving for the root or the approximate minimizer. This information about the root somehow affects that amount for the integration limits. Does this sound familiar to anyone that might help explain the concept better? Maybe give a textbook reference?
I think that the video solved for the minimizer and then also took the derivative the of complicated function to create an integral.
There was more mentioned in the context of integrating a function that can't be solved and the root in the exponent had to be approximated, in an effort to integrate over a minimum.
Thank you for all help and any references.
psi_1 = c_1 * e^-||x-x1|| psi_2 = c_2 * e^-||x-x2||
integrate psi_1 * psi_2
x1 = -a/2 x2 = +a/2
But centered on x1... Now, x1 = 0 x2 = -3/2a
Multiply it out and transfer to polar coordinates: e^-sqrt(r^2 -3rcos(theta)a + 9/4a^2)