How Do You Integrate a Wave Function to Find Electron Probability?

[bemigh]

Hey. I am pretty confident i have solve this problem. I just solve the integral of the given wave function, with the given limits... However, I am having a difficult time integrating it. The sqrt(2/L) can be brought outside of the integral, but what can i with the sin function?


The wave function of an electron is
ψ2(x) = sqrt(2/L) sin(2πx/L)
Calculate the probability of finding the electron between x = 0 and x = L/6.

Cheers

 

[dextercioby]

So what is the problem...?Compute the probability density first,and then integrate the result between the 2 limits specified in the problem...

Daniel.

 

[Data]

One-dimensional infinite square well I assume. What's wrong?

$$\psi_2 (x) = \sqrt{\frac{2}{L}} \sin{\frac{2\pi x}{L}} \Longrightarrow | \psi_2(x) |^2 = \frac{2}{L}\sin^2{\frac{2\pi x}{L}}$$

integrate from $0$ to $\frac{L}{6}$... If you don't remember the half-angle identity, here it is:

$$\sin^2{x} = \frac{1}{2}(1-\cos{2x})$$