Maximizing Localization in Adding Multiple Plane Waves

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Homework Help Overview

The discussion revolves around an assignment in quantum mechanics focused on adding multiple plane waves, specifically using the equation y(x) = Σ^n _i=1 Ai sin(ki X). The original poster seeks guidance on how to choose amplitudes and wave numbers to achieve maximum localization of the wave packet.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses difficulty in understanding how to effectively add multiple plane waves and select appropriate parameters for localization. Some participants inquire about the specific challenges faced, while others suggest straightforward approaches to the problem.

Discussion Status

The conversation is ongoing, with some participants providing basic suggestions regarding the selection of amplitudes and wave vectors, but no consensus or detailed methods have been established yet. The original poster has indicated partial understanding of one aspect of the assignment.

Contextual Notes

The original poster mentions a lack of available resources and guidance from their professor, which may contribute to the challenges faced in the assignment.

lilipoli
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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?
 

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What part are you having trouble with?
 
The first point of the assignment (addition of multiple plane waves). The second I have figured out already :)
 
They give you the equation. Just pick your amplitudes A and wave vectors k and evaluate the equation at positions x.
 

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