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Nathanael A. Fortune edited Appendix.tex
over 8 years ago
Commit id: 512130c9abecd6b827909b9f08c8a467df41208e
deletions | additions
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$$\Delta E_{n}=E_{n}-E_{n-1}$$
$$\Delta E_{n}=n(E_{a}+\delta_{n})-(n-1)(E_{a}+\delta_{n-1})$$
$$\Delta E_{n}=n(E_{a}+n\frac{\lambda}{L} E_{a})-(n-1)(E_{a}+(n-1)\frac{\lambda}{L} E_{a})$$
$$\Delta E_{n}=E_{a}\frac{\lambda}{L}
(2n-1)+E_{a}$$ (*) (2n-1)+E_{a} (*)$$
Therefore, when n=$\frac{1}{2}$:
$$\Delta E_{n}=E_{a}$$
In other words: