# Calculating the Hermite functions

The Hermite functions appear as the solutions of the quantum mechanical harmonic oscillator. But they have applications in many other fields and applications, e.g., pseudospectral methods. The Hermite functions $h_n(x)$ are defined as\begin{equation}\label{eq:h}h_n(x) = \frac{1}{\sqrt{\sqrt{\pi} 2^n n!}} \mathrm{e}^{-x^2/2} H_n(x) \,,\end{equation} where $H_n(x)$ denotes the $n$th Hermite polynomial defined via the recurrence relation\begin{equation}H_{n}(x) = 2xH_{n-1}(x)-2(n-1)H_{n-2}(x)\end{equation} with… Continue reading Calculating the Hermite functions