Schrödinger Wavefunctions in a Continuously Varying Potential

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send