# Electron in a Nanocrystal Modeled by a Quantum Particle in a Sphere

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This Demonstration shows the quantum effects observed on a single electron trapped in a spherical nanoparticle (also called a "quantum dot"), modeled as a particle in a sphere. We obtain the relationships among quantum energy levels , the radius of the nanoparticle , and the distance of the electron from the center of the nanoparticle by solving the Schrödinger equation. For spherical symmetry, with and :

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Contributed by: Yezhi Jin, Kyle Smola, Rahil Ukani (December 2016)

Additional contributions by: Eitan Geva (University of Michigan)

Open content licensed under CC BY-NC-SA

## Details

Reference

[1] T. Kippeny, L. A. Swafford and S. J. Rosenthal, "Semiconductor Nanocrystals: A Powerful Visual Aid for Introducing the Particle in a Box," *Journal of Chemical Education*, 79(9), 2002 pp. 1094–1100. doi:10.1021/ed079p1094.

Submission from the Compute-to-Learn course at the University of Michigan.

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