# Quantum Particle in a Regular Polygon by Finite Element Method

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The two-dimensional Schrödinger equation for a particle confined to a regular -gon (with ) can be written (in atomic units )

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Contributed by: S. M. Blinder (August 2022)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Test for particle in a square. Exact solution:

.

Comparison with finite element method:

(), (), (), (), (, ).

Reference

[1] Wikipedia. "Finite Element Method." (Jul 1, 2022). en.wikipedia.org/wiki/Finite_element_method.

## Permanent Citation