Two Dimensional Quantum Mechanical Scattering using Perfectly Matched Layers

Reynolds, Tyler K

Student Work

Two Dimensional Quantum Mechanical Scattering using Perfectly Matched Layers

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We consider a new way of looking at quantum mechanical scattering, motivated by the need for a framework that would allow calculations within complex waveguide geometries and for small scale systems. The two dimensional scattering problem is considered as a variational problem. This allows the use of the finite element method, which discretizes the region of interest so that numerical results may be obtained. We introduce stealth finite elements at the ends of a waveguide which serve to attenuate the wave. We demonstrate the numerical power of this framework by considering complicated scattering centers within waveguides. A modal analysis is performed on the resulting scattered waves.

This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

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