Quantum Well Explorer
This demonstrates probability distributions in quantum wells. The well is plotted in orange and the probability distribution is shown in blue. The blue line gives the energy of the bound state. Pick different potentials and use the slider to control the initial guess for the energy of the bound state. This initial guess is used by a shooting algorithm to find the eigenstates. Values at the low end of the slider bar will give the ground state while larger values will give excited states.
Snapshot 1: the probability distribution for the ground state in a "hat" potential
Snapshot 2: the probability distribution for the ground state in a triangular potential
Snapshot 3: the probability distribution for the first excited state asymmetric well