- #1

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I have a question about how to write down the following problem in a thesis.

I have a standing sinusodial wave with amplitude:

[tex]|\hat{q}_n|[/tex]

which I want to express as superposition of two traveling waves. Would you suggest do write the sum in the last line like I did, or has somebody a better idea?

[tex]

\DeclareMathOperator{\e}{e}

\begin{split}

w &= |\hat{q}_n| \sin(n\pi x/L) \e^{i\omega t} \\

&= |\hat{q}_n| \frac{1}{2i}(\e^{i n \pi x/L} - \overline{\e^{i n \pi x/L}}) \e^{i\omega t} \\

&= |\hat{q}_n| \e^{i\omega t} \sum_{\nu = \pm n} \frac{\nu}{2i} \e^{i \nu \pi x/L} \; .

\end{split}

[/tex]

Thanks!