Finding Normalization Constant for Wave Function in Limited Space?

[atomicpedals]

Homework Statement

A particle may be represented in the space, $-a \le x \le a$, by the wave function $\Psi (x) = A cos(\frac{\pi x}{2a})$. Find the normalization constant

Homework Equations

$$\int |\Psi (x)|^{2}dx=1$$

The Attempt at a Solution

In reading the question it defines the space as being $-a \le x \le a$ does this in-turn change the limits of integration for the normalization from +/- infinity to +/- a? And so result in:

$$\int |A cos(\frac{\pi x}{2a})|^{2}dx=1$$
$$A^{2}a=1$$
$$A = (\frac{1}{a})^{1/2}$$

 

[vela]

Yes, that's correct.