[Physics] How to normalize this wavefunction?

homework-and-exercisesnormalizationquantum mechanicswavefunction

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.

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