Maximizing Localization in Adding Multiple Plane Waves

[lilipoli]

To whom it may concern,

I am having issues with a given assignment in my quantum mechanics class. The instructions listed below are all I have to go on since the prof. is not available for discussion and I have searched through at least 15 articles regarding plane waves and a dozen textbooks and still come up empty on how to definitively add multiple plane waves. I wouldn't be posting on a forum, if I were not to try everything else beforehand myself.
Any help is greatly appreciated and I apologize for my bad English.-Write a program for adding two or more plane waves [equation: y(x) = Σ^n _i=1 Ai sin(ki X) ]
-How to choose amplitudes Ai and wave numbers ki for any given n so that the wave packet is as localized as possible?

 

[marcusl]

What part are you having trouble with?

 

[lilipoli]

The first point of the assignment (addition of multiple plane waves). The second I have figured out already :)

 

[marcusl]

They give you the equation. Just pick your amplitudes A and wave vectors k and evaluate the equation at positions x.