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For Educators · Particle in a Box

Particle in a Box for an atom trap

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate an atom trap live below — adjust the inputs and watch it respond, right in your browser.

Particle in a BoxLive

quantized energy levels

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Quantum number n

Well width L (nm)

Show probability density

Confine a quantum particle to a box and its energy can only take discrete values, E_n = n²h²/8mL². The wavefunctions are standing waves with n humps; squaring them gives the probability of finding the particle at each point. Narrowing the box pushes the energy levels dramatically higher — quantum confinement.

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Data Inspector

Energy Eₙ3.384 eV

Level n3

Nodes2

Governing equation

E_{3} = \frac{3 ^{2} h ^{2}}{8 m L ^{2}} = 3.384 eV, ψ_{3} = \frac{2}{L} sin \frac{3 π x}{L}, L = 1 nm

Reading this result: Level n=3 carries 2 interior nodes, and because energy scales as n² it sits 9× above the ground state of this same well.

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Frequently asked questions

Is this good for educators?: Yes — this version of "Particle in a Box for an atom trap" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.