# 5: Particle in Boxes

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The complexities of quantum mechanics are demonstrated mostly in trapped particles.

• Free-Electron Model
The particle in a box quantum-mechanical problem can provide an instructive application to chemistry: the free-electron model (FEM) for delocalized π -electrons.
• Particle in a 1-Dimensional box
A particle in a 1-dimensional box is a fundamental quantum mechanical approximation describing the translational motion of a single particle confined inside an infinitely deep well from which it cannot escape.
• Particle in a 2-Dimensional Box
A particle in a 2-dimensional box is a fundamental quantum mechanical approximation describing the translational motion of a single particle confined inside an infinitely deep well from which it cannot escape.
• Particle in a 3-Dimensional box
A particle in a 3-dimensional box is a fundamental quantum mechanical approximation describing the translational motion of a single particle confined inside an infinitely deep well from which it cannot escape.
• Particle in a Sphere
Particle on a sphere is one out of the two models that describe rotational motion. A single particle travels on the surface of the sphere. Unlike particle in a box, the particle on a sphere requires angular momentum, J.
• Particle on a Ring
The case of a particle in a one-dimensional ring is similar to the particle in a box.

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