Expansion of Hydrogen GS (Relativistic)

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SUMMARY

The forum discussion centers on verifying equations 16 and 17 from a specific paper regarding the expansion of Hydrogen GS in a relativistic context. The user encountered discrepancies in their results when using Mathematica, specifically noting the absence of a factor of 1/2 in equation 16. Another participant successfully reproduced the factor using WolframAlpha, indicating a potential typo in the original user's equation. This highlights the importance of careful verification in mathematical computations.

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sean_mp
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Homework Statement


I'm trying to verify equations 16 and 17 on the attached paper, but I'm just not getting the same values they are. I've used mathematica and it just isn't happening. For one thing, there should be a factor of 1/2 in front of equation 16, but I'm really not seeing how they got this from a typical series expansion.

Homework Equations


I need help getting the same values as 16 and 17 in the paper. I'm just not getting it in my output.


The Attempt at a Solution

 

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I don't have a lot to add, other than I plugged (14) into WolframAlpha and reproduced your factor of 1/2 (http://www.wolframalpha.com/input/?i=series+sqrt%281-+g%2F%28sqrt%28k^2%2Bg%29%2Bn-k%29^2%29+in+g+to+order+2). I have no idea why he gets something else.
 
Wow... I'm embarrassed that I didn't get this myself... I must have had a typo in my equation or something.

Thanks a lot, you're a lifesaver.
 

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