deletions | additions       diff --git a/Appendix.tex b/Appendix.tex  index 2ec3c10..4d1d5ab 100644  --- a/Appendix.tex  +++ b/Appendix.tex 
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$$E_{n}=n(E_{a}+\delta_{n})$$  $$\delta_{n}=n\frac{\lambda}{L} E_{a}$$  Plugging into:  $$\Delta_{E_{n}}=E_{n}-E_{n-1}$$  $$\Delta_{E_{n}}=n(E_{a}+\delta_{n})-(n-1)(E_{a}+\delta_{n-1})$$  $$\Delta_{E_{n}}=n(E_{a}+n\frac{\lambda}{L} $$\Delta E_{n}=E_{n}-E_{n-1}$$  $$\Delta E_{n}=n(E_{a}+\delta_{n})-(n-1)(E_{a}+\delta_{n-1})$$  $$\Delta E_{n}=n(E_{a}+n\frac{\lambda}{L}  E_{a})-(n-1)(E_{a}+(n-1)\frac{\lambda}{L} E_{a})$$ $$\Delta_{E_{n}}=E_{a}\frac{\lambda}{L} $$\Delta E_{n}=E_{a}\frac{\lambda}{L}  (2n-1)+E_{a}$$ Therefore, when n=$\frac{1}{2}$:  $$\Delta_{E_{n}}=E_{a}$$  In other words: