QM 1D energy eigenstates with variational solution
This interactive application integrates the time-independent Schrodinger equation. It also allows comparison between the actual solution and variational solutions.
You can select one of two potential energy functions, choose the symmetry of the desired solution, and adjust the energy of the state. Acceptable quantum bound states must go asymptotically to zero in the classically forbidden regions at large positive and negative x. Adjust the energy until that condition is (approximately) reached to find the energy eigenvalues and eigenstates. Choose the variational option to find the lowest energy for a Gaussian and (for ground state) a truncated cosine-squared wave function.
R. Tobin, Created with GeoGebra