Understanding Regular and Outgoing Functions in Vector Spherical Wave Functions

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Discussion Overview

The discussion revolves around the concepts of "regular" and "outgoing" functions in the context of vector spherical wave functions, particularly as they relate to the solutions of wave equations. Participants seek clarification on these terms and their implications in electrodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the definitions of "regular function" and "outgoing function" as mentioned in a research paper.
  • Another participant emphasizes the importance of boundary conditions in wave equations, noting that these conditions determine whether a wave is incoming or outgoing.
  • A mathematical example is provided, illustrating the solutions to a scalar wave equation and how the choice of signs in the solutions corresponds to incoming and outgoing waves.
  • There is a question about whether "regular" is synonymous with "incoming" and the reasoning behind the terminology used.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the terms "regular" and "outgoing," and there is no consensus on whether "regular" is equivalent to "incoming." The discussion remains unresolved regarding the definitions and implications of these terms.

Contextual Notes

The discussion references specific mathematical forms of wave equations and their solutions, but lacks clarity on the definitions of "regular" and "outgoing" functions as used in the referenced paper. There are also indications of potential singularities in the solutions at certain points.

Who May Find This Useful

Readers interested in wave equations, electrodynamics, and the mathematical treatment of spherical wave functions may find this discussion relevant.

OKY
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I am reading reasearch paper about electrodynamic wave.

In the paper, there is a following description
1. regular function
2. outgoing function

They seem to be related to vector spherical wave function.

What is the "regular function" and "outgoing function"?

I would like to know the book in which I can understand about them.


Best regards
 
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Could you show us the paper? A context would be valuable.
 
When you solve the wave equation (any wave equation - scalar, vector, etc) you must set a boundary condition that says whether the wave is incoming or outgoing. The simplest example is the scalar wave equation with spherical symmetry,

1/r ∂2/∂r2 (rφ) - 1/c22φ/∂t2 = 0

The solutions are φ(r,t) = A/r exp i(kx + ωt) + B/r exp i(kx - ωt). If you choose the + sign, the solution is incoming. The - sign is an outgoing solution. Both of them are singular at r = 0, but the solution with A = -B is regular there.
 
Polyrhythmic said:
Could you show us the paper? A context would be valuable.


The paper (manual document) can be obtained from
the link to "manual" in the below web site.
http://eng.auburn.edu/users/dmckwski/scatcodes/

Around page 4 and 5, they use "regular" and "outgoing".


Thank you in advance.
 
Bill_K said:
When you solve the wave equation (any wave equation - scalar, vector, etc) you must set a boundary condition that says whether the wave is incoming or outgoing. The simplest example is the scalar wave equation with spherical symmetry,

1/r ∂2/∂r2 (rφ) - 1/c22φ/∂t2 = 0

The solutions are φ(r,t) = A/r exp i(kx + ωt) + B/r exp i(kx - ωt). If you choose the + sign, the solution is incoming. The - sign is an outgoing solution. Both of them are singular at r = 0, but the solution with A = -B is regular there.

Thank you very much for the detailed reply.

So, is the "regular" same as "incoming" wave? Why they call "regular"?
 

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