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.