I don't know the name of this but it seems that I have some kind of a problem solving illness. It has happened many times in my life that my close friends make fun of it from time to time. The problem is, sometimes when I think about something, its not the simplest solution that comes to my mind and its the more complicated solutions that comes to my mind first!(adsbygoogle = window.adsbygoogle || []).push({});

For example today someone asked me how to prove that the degeneracy of hydrogen atom energy levels(not considering fine structure) is ##n^2##. The solution is to compute the sum ## \displaystyle \sum_{l=0}^{n-1} (2l+1) ##. And this is what I sent him:

## \displaystyle \sum_{l=0}^{n-1} (2l+1)=\sum_{l=0}^{2n-1} l-\sum_{l=0}^{n-1} 2l=n(2n-1)-n(n-1)=2n^2-n-n^2+n=n^2 ##

But, there is an easier way to do the sum:

## \displaystyle \sum_{l=0}^{n-1} (2l+1)=2\sum_{l=0}^{n-1} l+\sum_{l=0}^{n-1} 1=n(n-1)+n=n^2##.

What is this illness? How can I cure it?

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# How can I cure this?

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