How Do You Normalize a Wave Function with Given Boundaries?

[darkfall13]

[SOLVED] Normalization of wave functions

Mainly my question is that with the normalization of a wave function in quantum mechanics we use $$\int_\infty^\infty |\Psi(x,t)|^2 dx = 1$$ and we can solve for a constant we may have been given in the problem.

Homework Statement

Determine normalization constant:

$$\Psi(x) = A\cos{\frac{2\pi{x}}{L}}$$ for $$\frac{-L}{4} \leq x \leq \frac{L}{4}$$ and $$\Psi = 0$$ elsewhere

Homework Equations

The Attempt at a Solution

I'm wondering if I'm given those boundaries because we can replace the infinities in the normal equation with these boundaries or would they be used for something else? Thank you!

 

[siddharth]

I'm wondering if I'm given those boundaries because we can replace the infinities in the normal equation with these boundaries or would they be used for something else? Thank you!

Outside those boundaries, the value of $$\Psi(x)$$ is 0, as is stated in your post.

So, only the part between -L/4 and L/4 will contribute to the integral.

 

[darkfall13]

Ah ok thanks!

 

[vincebs]

Be sure to mark down this thread as SOLVED once you've gotten the answer.