OBSERVATION CHAMBER / ACTIVE
Quantum Tunneling Observatory
Change a finite barrier and observe the connected quantum wave, transmitted flux, and reflected flux in stationary scattering.
01 / OBSERVE THE WAVE
A wave connects across the barrier
Drag: horizontal = width L, vertical = height V₀. Canvas keys: ← → L, ↑ ↓ V₀, Space/P run or pause, S step, R reset.
E < V₀
- Transmission T
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- Reflection R
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- Net current j
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- |T + R − 1|
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- Interface |Δψ| max
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- Interface |Δψ′| max
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03 / RECORD THE OBSERVATION
Keep this scattering state
Reports and PNG images record the current settings and pause phase animation. RESET clears generated outputs.
Download PNGGenerated report
OBSERVATION MODEL
One finite, real barrier
The potential is V₀ for 0 ≤ x ≤ L and zero on both sides. Assume E > 0, V₀ ≥ 0, L ≥ 0, and dimensionless ℏ = m = 1. The incident plane wave has unit amplitude; |ψ|² is relative density, not a normalized packet probability.
This is stationary scattering without absorption. It does not predict tunneling time or simulate individual particle trajectories.
FORMULA / CONTINUITY
Match both ψ and its derivative
k = √(2E), q² = 2(E − V₀)
ψleft = exp(ikx) + r exp(−ikx)
ψright = tL exp(ik(x − L))
T = |tL|², R = |r|²
j = Im(ψ*ψ′) = kT = k(1 − R)
At E = V₀ the interior wave is linear and T = 1 / (1 + EL²/2). Below the barrier, scaled exponentials avoid overflow. Both interface residuals are recomputed from the waves on each side.
Richard Fitzpatrick / Square Potential BarrierHOW TO OBSERVE
Three controlled comparisons
- Keep E = 0.50 and V₀ = 1. Increase L: the transmitted flux falls while the interior wave decays.
- Set E = V₀ = L = 1. Transmission is 2/3, with no division by zero at the threshold.
- Set V₀ or L to zero: T = 1 and R = 0. Switch to density or current; phase animation does not move these stationary quantities.
CHECK THE NUMERICS
Analytic fixtures and conservation
Checks include T = 0.419974341614 at E = 0.5, the threshold T = 2/3, and resonance T = 1 at E = 1 + π²/2, all with V₀ = L = 1. A separate probability formula checks the complex-amplitude solution.
Not runOBSERVATION POLICY
This chamber calculates stationary scattering by one real rectangular barrier in your browser. Inputs, reports, and images stay local. It does not measure particles or simulate a time-dependent wave packet.
Route
This chamber belongs to Fields in Motion.
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