- #1
MarkoA
- 12
- 1
Hi,
I have a question about how to write down the following problem in a thesis.
I have a standing sinusodial wave with amplitude:
|\hat{q}_n|
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?
<br /> \DeclareMathOperator{\e}{e}<br /> \begin{split}<br /> w &= |\hat{q}_n| \sin(n\pi x/L) \e^{i\omega t} \\<br /> &= |\hat{q}_n| \frac{1}{2i}(\e^{i n \pi x/L} - \overline{\e^{i n \pi x/L}}) \e^{i\omega t} \\<br /> &= |\hat{q}_n| \e^{i\omega t} \sum_{\nu = \pm n} \frac{\nu}{2i} \e^{i \nu \pi x/L} \; .<br /> \end{split}<br />
Thanks!
I have a question about how to write down the following problem in a thesis.
I have a standing sinusodial wave with amplitude:
|\hat{q}_n|
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?
<br /> \DeclareMathOperator{\e}{e}<br /> \begin{split}<br /> w &= |\hat{q}_n| \sin(n\pi x/L) \e^{i\omega t} \\<br /> &= |\hat{q}_n| \frac{1}{2i}(\e^{i n \pi x/L} - \overline{\e^{i n \pi x/L}}) \e^{i\omega t} \\<br /> &= |\hat{q}_n| \e^{i\omega t} \sum_{\nu = \pm n} \frac{\nu}{2i} \e^{i \nu \pi x/L} \; .<br /> \end{split}<br />
Thanks!