rayman123
Apr27-10, 07:03 AM
1. The problem statement, all variables and given/known data
find the normalisation constant (A)
2. Relevant equations
wave functcion
\psi (x,t)= A[3sin(\frac{\pi x}{L})+2sin(\frac{2\pi x}{L}]
3. The attempt at a solution
A^2\int_{0}^{L}[\psi(x,t)]^2dx=1
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
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
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
is it correct so far?
from the last integral i got
A^2\frac{L}{\2\pi}\int_{0}^{2\pi}4sin^2(2t)dt=A^22 L
i dont have a good idea for solving the second intregral....
find the normalisation constant (A)
2. Relevant equations
wave functcion
\psi (x,t)= A[3sin(\frac{\pi x}{L})+2sin(\frac{2\pi x}{L}]
3. The attempt at a solution
A^2\int_{0}^{L}[\psi(x,t)]^2dx=1
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
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
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
is it correct so far?
from the last integral i got
A^2\frac{L}{\2\pi}\int_{0}^{2\pi}4sin^2(2t)dt=A^22 L
i dont have a good idea for solving the second intregral....