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Question Number 138828 by BHOOPENDRA last updated on 18/Apr/21

Answered by Dwaipayan Shikari last updated on 22/Apr/21

$$\mathrm{\Psi }=Asin\frac{\pi x}{l}$$$${\int }_0^l\mid \mathrm{\Psi }{\mid }^{2}dx=1\Rightarrow {\int }_0^l{A}^2{sin}^2\frac{\pi x}{l}dx=1\frac{\pi x}{l}=u\Rightarrow 1=\frac{l}{\pi }.\frac{du}{dx}$$$$\Rightarrow A^2\frac{l}{\pi }{\int }_0^{\pi }{sin}^{2}udu=1$$$$\Rightarrow A^2\left(\frac{\pi }{2}\right)=\frac{\pi }{l}\Rightarrow A=\sqrt{\frac{2}{l}}$$

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