 Finite-well bound-state node sequence

For a symmetric one-dimensional finite square well, nondegenerate bound states alternate even and odd parity, starting with an even ground state. The $n$th state counted from zero has $n$ interior nodes. Outside the well, it decays with inverse length $\sqrt{2m(U-E_n)}/\hslash$. Matching both the wavefunction and its first derivative at a finite step distinguishes it from the infinite-well approximation.