# Particles in 1D and 3D Boxes

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This Demonstration treats the quantum-mechanical problems of a particle in a box. We consider both the one-dimensional and three-dimensional cases. For both, we show diagrams that depict the probability density and energy of the particle. These values/graphics depend on the energy level of the particle and the dimensions of the boxes. These variables can be manipulated to show how they influence the behavior of a particle in a box. For the 1D box, the energy levels are given by , where the quantum number has the possible values . For the 3D box, , where a, b and c are the length, width and height of the box, respectively, and , and are the associated quantum numbers.

Contributed by: Cassy Chen, Rasmi Davu and Isabelle Zelaya (October 2018)

Open content licensed under CC BY-NC-SA

## Details

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

Reference

[1] R. Chang, *Physical Chemistry for the Biosciences*, Sausalito, CA: University Science, 2005.

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## Permanent Citation