Solving Laplace of Plane Wave with x,y,z Coordinates: Troubleshooting Guide

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Homework Help Overview

The discussion revolves around the application of the Laplace operator to a plane wave in three-dimensional Cartesian coordinates. Participants are troubleshooting their understanding of the mathematical representation of this concept.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to express the Laplace operator and the plane wave in terms of Cartesian coordinates. Questions are raised about the specific components of the wave vector and the procedure for deriving the equations.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the procedure and specific equations. Some guidance has been offered regarding the components of the wave vector, but no consensus has been reached on the exact approach to take.

Contextual Notes

There appears to be some confusion regarding the transformation of the wave equation into Cartesian coordinates, and participants are questioning the assumptions underlying their current understanding.

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This is what I got for Nabla and Laplace of plane wave. I have problems when I try to write out it with x, y, z coordinates. Can somebody help me? Thanks!


http://img213.imageshack.us/img213/9532/85490316.jpg


http://img528.imageshack.us/img528/6835/f41cab97f649df5431127b5.png
 
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What problems do you have? You should get the same thing, just written in terms of the components of k and r.
 
@Muphrid

I know the result, but I have problems with procedure. Can you write down this equation; or just the start? Thanks!
 
What's k \cdot r when written in terms of cartesian coordinates?
 
Yes.
 

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