(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find the normalisation constant (A)

2. Relevant equations

wave functcion

[tex] \psi (x,t)= A[3sin(\frac{\pi x}{L})+2sin(\frac{2\pi x}{L}][/tex]

3. The attempt at a solution

[tex] A^2\int_{0}^{L}[\psi(x,t)]^2dx=1[/tex]

[tex] A^2\int_{0}^{L}[9sin^2(\frac{\pi x}{L})+12sin(\frac{\pi x}{L})sin(\frac{2\pi x}{L})+4sin^2(\frac{2\pi x}{L})}]dx[/tex]

1. The problem statement, all variables and given/known data

i try to solve each integral separately

I have started with the first one and i got

[tex] A^2\int_{0}^{L}[9sin^2(\frac{\pi x}{L})]dx= A^2\cdot \frac{9L}{ \pi}\int_{0}^{\pi}sin^2tdt=A^2\cdot \frac{9L}{\pi}[\frac{1}{2}t+\frac{sin(2t)}{4}]\right]_{0}^{\pi}=A^2\cdot \frac{9}{2}L[/tex]

is it correct so far?

from the last integral i got

[tex]A^2\frac{L}{\2\pi}\int_{0}^{2\pi}4sin^2(2t)dt=A^22L[/tex]

i dont have a good idea for solving the second intregral....

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# Homework Help: Wave funtion and normalisation constant

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