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For Students · Quantum Tunneling

Quantum Tunneling for a Bose-Einstein condensate

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a Bose-Einstein condensate live below — adjust the inputs and watch it respond, right in your browser.

Quantum TunnelingLive

through a barrier it cannot climb

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Particle energy E (eV)

Barrier height V (eV)

Barrier width (nm)

Classically a particle with less energy than a barrier is trapped. Quantum mechanically its wavefunction decays inside the barrier but does not vanish, so there is a finite chance it appears on the other side — tunneling. The probability falls off exponentially with barrier width and height, the principle behind scanning tunneling microscopes and nuclear fusion.

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Transmission T2.34e-6

Reflection R1.000

Regimetunneling

Governing equation

T \approx e^{- 2 κa} = 2.34 e - 6, κ = \frac{2 m ( V - E )}{ℏ} = \frac{2 m ( 5.0 - 3.0 )}{ℏ}, a = 0.50 nm

Reading this result: The barrier is thick and tall relative to the energy, so transmission is vanishingly small — essentially nothing gets through.

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Frequently asked questions

Is this good for students?: Yes — this version of "Quantum Tunneling for a Bose-Einstein condensate" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.