Equations with meaning
Eₙ = n²h² / (8mL²)n = 1, 2, 3… · Eₙ ∝ n²/(mL²)
ψₙ(x) = √(2/L) sin(nπx/L)ψ is zero at both walls.
Probability density = |Ψ(x,t)|²Probability in a region is the area under this curve.
Ψₙ(x,t) = ψₙ(x) exp(−iEₙt/ℏ)The phase changes; a single state's density does not.
Ψ = (Ψ₁ + Ψ₂) / √2Equal coherent superposition: P(E₁) = P(E₂) = ½.
⟨E⟩ = (E₁ + E₂) / 2An average is not an extra eigenvalue.
ΔE = Ef − EiThe energy supplied or removed equals the difference.
h: Planck constant · ℏ = h/(2π) · m: mass · L: box width · n: positive integer · x: position · t: physical time. 1 nm = 10⁻⁹ m; 1 eV = 1.602176634 × 10⁻¹⁹ J.
What this model does—and does not—show
This is the nonrelativistic, one-dimensional infinite square well. It is not a model of hydrogen shells or every quantum system. We display the first five of infinitely many bound states.
The chip, barriers, wiring, and readout instrument are recognizable schematic lab structures. They are not a calibrated device or a photograph. Real semiconductor barriers are finite and can permit tunnelling; here the walls are impenetrable.
Width and mass sliders compare equilibrium eigenstates. They do not simulate sudden boundary motion, real electron mass changes, or thermal effects. State preparation assumes external control; transition rates and selection rules are not calculated.
The purple and orange curves are real and imaginary wavefunction components; the green curve is probability density. Vertical curve amplitude is scaled for readability. Dots are independent preparation-and-detection outcomes, never a hidden particle trajectory. Position trials are restricted to a single eigenstate to keep one consistent predicted distribution.
The coherent superposition is (n = 1 + n = 2)/√2, not an incoherent statistical mixture. Ideal energy measurement projects it onto one eigenstate. Decoherence and detailed measurement hardware are not modeled.
Time is deliberately slowed by a fixed factor: 1 teaching second = 3.3 fs. The energy axis may rescale when needed; faint comparison ticks mark a previous setting during a size/mass demonstration.