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\section{Where to find data files, figures, tables, and notes}  Derivation of \ref{eq:lowestlevel}:\newline  We have:  $$E_{n}=n(E_{a}+\delta_{n})$$  $$\delta_{n}=n\frac{\lambda}{L} E_{a}$$  Plugging into:  $$\Delta_{E_{n}}=E_{n}-E_{n-1}$$  $$\Delta_{E_{n}}=n(E_{a}+\delta_{n})-(n-1)(E_{a}+\delta_{n-1})$$  $$\Delta_{E_{n}}=n(E_{a}+n\frac{\lambda}{L} E_{a})-(n-1)(E_{a}+(n-1)\frac{\lambda}{L} E_{a})$$