I need to find the normalisation constant $A$ for the wave function:

$$

\psi\left(x\right) = \left\{

\begin{array}{lr}

A &\: \frac{-a}{4} \leq x \leq \frac{a}{4}\\

0 &\: {\rm otherwise}

\end{array}

\right.

$$

Could I get a hint on answering this question?

I think I am supposed to use the following but I'm not sure.

$$ \int_{-\infty}^{\infty} \left|\psi\left(x\right)\right|^2 \, dx = 1$$

## Best Answer

$\newcommand{\d}{\;\mathrm{d}}$You should straightforward take the integral that you mentioned:

$$\int_{-\infty}^\infty \left| \psi\right|^2 \d x =\int_{-a/4}^{a/4} AA^* \d x + \int_{-\infty}^{-a/4} 0 \d x + \int_{a/4}^\infty 0 \d x =1$$

I won't do the integral and calculate $A$ because it is trivial to do therefore I leave the rest to you.