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## Homework Statement

## Homework Equations

## The Attempt at a Solution

So we want sine in terms of the exponentials when we take the Fourier transform [tex]F(k)=\int_{-\infty}^{\infty}f(x)e^{-ikx}dx[/tex] where [itex]f(x)=\sin(3\pi x/L)[/itex]. Let a=3pi/L. Then [tex]\sin(ax)=\frac{e^{iax}-e^{-iax}}{2i}[/tex].

(Is this correct?)

Then we can take the Fourier transform:

[tex]F(k)=\int_{-\infty}^{\infty}\frac{e^{iax}-e^{-iax}}{2i}e^{-ikx}dx[/tex]. Rearranging gives [tex]\frac{1}{2i}[\delta(K+a)-\delta(K-a)][/tex]. But my notes says there is [itex]\sqrt{2\pi}[/itex] in front and I'm not sure where it came from?

Any help will be appreciated.