# Normalization

Numerical normalization is complicated by the discretization of the x-axis.

To see this, discretize the normalisation-condition $\int_{-\infty}^{\infty} |\psi(x)|^2 dx = 1$. The discrete version is $\sum_{n=0}^N |\psi(x_n)|^2 \Delta x = 1 => \sum_{n=0}^N |\psi(x_n)|^2 = \frac{1}{\sqrt{\Delta x}}$. So the analytical wavefunctions must be normalized to $\frac{1}{\sqrt{\Delta x}}$ instead of to 1.

The composer takes care of that.