Schrödinger Wavefunctions in a Continuously Varying Potential

This Demonstration shows solutions of the one-dimensional Schrödinger equation in a potential-energy field , which can be varied by moving a series of locators. A quantum number (from 1 to 20) can be selected. The Schrödinger equation is then solved numerically for the wavefunctions , which are plotted in red, in arbitrary units. The black curves show the corresponding probability densities . The potential energy is scaled in units of .