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 .
The snapshots show that a small change in the potential can result in a very large variation of the wavefunction.
 A. Messiah, Quantum Mechanics, New York: John Wiley & Sons, 1958.
 R. Shankar, Principles of Quantum Mechanics, 2nd ed., New York: Plenum, 1994.