Argand Phasor Plane
Complex Space
Relative Phase Δφ (Phase Shift)
180°
Amplitude |a₁| (Cyan Vector)
1.00
Amplitude |a₂| (Magenta Vector)
1.00
Spatial Wavefunction & Particle Detector Screen
|Ψ(x)|² Density
Spatial Frequency k (Fringe Density)
2.50
Interference Regime
Complete Destructive
Total Real Re(Ψ)
0.000
Total Imaginary Im(Ψ)
0.000
Center Magnitude |Ψ(0)|
0.000
Center Prob. Density |Ψ(0)|²
0.000
Detector Accumulation
0 Hits
ψ₁ = |a₁|e^(iφ₁) +
ψ₂ = |a₂|e^(iφ₂) ⟹
Ψ_total = ψ₁ + ψ₂
Ψ = (1.00 + 0.00i) + (-1.00 + 0.00i) = 0.00 + 0.00i
P(x) = |Ψ(x)|² = |ψ₁(x) + ψ₂(x)|² ≠ |ψ₁|² + |ψ₂|² (Interference Term Active)
Core Quantum Principle: In quantum mechanics, probability amplitudes are complex vectors that add linearly before calculating probabilities. When relative phase Δφ = 180°, amplitudes cancel perfectly (Ψ = 0) at interference nodes. Destructive interference does not destroy quantum probability; it redistributes detection events to regions where amplitudes align constructively.