# Schrödinger Wavefunctions in a Continuously Varying Potential

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .

Contributed by: Srivishnupreeth Rendla (July 2016)

With additional contributions by: Robert Morris

(Wolfram Summer Camp 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The snapshots show that a small change in the potential can result in a very large variation of the wavefunction.

References

[1] A. Messiah, *Quantum Mechanics*, New York: John Wiley & Sons, 1958.

[2] R. Shankar, *Principles of Quantum Mechanics*, 2nd ed., New York: Plenum, 1994.