I Expansion of 1/|x-x'| into Legendre Polynomials

AI Thread Summary
The discussion centers on the expansion of the function 1/|x - x'| using Legendre polynomials and geometric series. There is confusion regarding the equivalence of this function to two different expressions based on the values of x and x'. It is clarified that the function is not equal to both expressions simultaneously; rather, it depends on which variable is larger. The expression involving Θ(x - x') serves to summarize the two cases succinctly. Understanding this distinction is crucial for proper application in the context of the discussion.
deuteron
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we know that we can expand the following function in Legendre polynomials in the following way
1712516696799.png

in the script given yo us by my professor, ##\frac 1 {|\vec x -\vec x'|}## is expanded using geometric series in the following way:


1712516763072.png


However, I don't understand how ##\frac 1 {|\vec x -\vec x'|}## is equal to both the above, and the below:

1712517015521.png
 
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Do you understand the meaning of ##\Theta(x-x')##?
It's not equal to both. It's equal to one or the other depending on which of ##x## and ##x'## is larger. The bottom expression summarizes in one line the two "für" cases above it.
 

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