## Quantum-Mechanical Diffraction andInterference Patterns for Sharp-Edged Slits

*W. P. Healy*

`liam.healy@rmit.edu.au`

Department of Mathematics

**RMIT University**

*R. A. Samandra*

Department of Mathematics

**RMIT University**

Austalia

### Abstract

Quantum-mechanical diffraction and interference patterns associated with one imensional motion of a non-relativistic particle are obtained by using Maple. The normalized probability density for the particle's position after passage of the wave function through one or more sharp edged slits involves combinations of Fresnel cosine and sine integrals and can readily be plotted. The Aharonov-Bohm phase shift caused by a magnetic flux string located between two slits is also considered. The periodicity of the Aharonov-Bohm effect is verified in a Maple animation in which the interference pattern varies with the value of the confined magnetic flux. The classical limit is demonstrated in a separate animation in which Planck's constant is made to approach zero and it is shown that the Aharonov-Bohm effect vanishes in this limit.

©1999. ATCM, Inc