The present bound states lab computes the parabolic confinement potential wavefunctions end eigenstates numerically. Unlike the square well case which mimics a finite potential well and has different eigenvalues and eigenfunctions from the infinite square well, one would expect this parabolic case to deliver the same results as the analytical case.

That is only true in the limit if the discretzation is in the parabolic regime. So for studying the impact of the numerical tight bonding dispaersion it would also be interesting to compare this numerical result to the explicit analytical result. Also the analytical result might run just faster. Who knows. Definitions of Hermite polynomials can be found here: http://en.wikipedia.org/wiki/Hermite_polynomials the eigen energies of the parabolic confinement are of course trivial.