I am trying to find the solution to a problem defined as follows:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

(\partial_x^2-K^2)^2 G(\vec{x},\vec{x}')=\delta(\vec{x}'-\vec{x})

[/tex]

where K is simply a constant and x is three dimensional.

[tex]

A \left[ e^{-K(\vec{x}-\vec{x}')}H(\vec{x}-\vec{x}') + e^{K(\vec{x}-\vec{x}')}H(\vec{x}'-\vec{x}) \right]

+ B \left[ (\vec{x}-\vec{x}') e^{-K(\vec{x}-\vec{x}')}H(\vec{x}-\vec{x}') + (\vec{x}'-\vec{x}) e^{K(\vec{x}-\vec{x}')}H(\vec{x}'-\vec{x}) \right]

[/tex]

Here, H is the step function.

and I am trying to find A and B such that the first equation is satisfied. Does anyone have any advice on how to proceed?

My initial guess was to apply [tex] (\partial_x^2-K^2)^2 [/tex] to my proposed solution and then solve for A and B. This gets a bit tricky since once I start taking derivatives I get derivatives of the delta function.

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# Help with a Helmholtz-like equation

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