Let $I=(a,b)$ be a bounded interval, let $V\in C(I;\mathbb R)$ extend continuously to $[a,b]$, and let \begin{align*} H=-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+V \end{align*} be the associated regular self-adjoint Schrödinger operator on $L^2(I)$ with separated self-adjoint boundary conditions at $a$ and $b$. Suppose its eigenvalues are ordered increasingly as \begin{align*} E_1<E_2<E_3<\cdots. \end{align*} Then the $n$th eigenfunction has exactly $n-1$ nodes in the interior of the interval.