Infinite square-well spectrum University Quantum Mechanics I · Infinite square well
Well Architect
Build an electron well whose quantised levels or level gaps match a spectral gate.
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Challenge 1 of 3
Build a ground-state well
An electron occupies n = 1. Change the confinement width to tune its nonzero ground-state energy.
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Place the ground level between 0.90 and 1.10 eV.
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Connect confinement width and integer mode number with n-squared energy levels, nodes and differences between energy eigenvalues.
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The physics behind the game
Connect confinement width and integer mode number with n-squared energy levels, nodes and differences between energy eigenvalues.
Eₙ = π²ℏ²n²/(2mₑL²) = 0.376030 n²/Lₙₘ² eV; n = 1, 2, 3, …
Model assumptions. A nonrelativistic electron in a one-dimensional well with infinitely high walls. The interior potential is zero. Density is |ψₙ|², with n−1 interior wavefunction nodes; it is not an electron path. Level differences are energy gaps only: selection rules, transition rates and finite-barrier penetration are outside the model.