Mathematical Representation
Stage 1: The Formula
H =
∑
εi
|i⟩⟨i|
+
∑
Jij
|i⟩⟨j|
The Hamiltonian (H) represents the system's total energy, composed of independent node energies (ε) and coupling channels (J).
|1⟩
|2⟩
|3⟩
⟨1|
ε₁
1.50
J₁₂
0.80
J₁₃
0.20
⟨2|
J₂₁
0.80
ε₂
1.20
J₂₃
0.60
⟨3|
J₃₁
0.20
J₃₂
0.60
ε₃
0.70
💡 Click any diagonal node (ε) or connector (J) cell to adjust values below.
Click 'Mutate Matrix' to expand Dirac notation.
Interactive Matrix Parameters
Site Energies (ε)
1.5 eV
1.2 eV
0.7 eV
Coupling Constants (J)
0.8 eV
0.6 eV
0.2 eV
Physical Quantum Field Grid
Simulating site potentials as glowing wells and couplers (J) as rigid physical connections.
Exciton Mode:
Coherent
Propagation:
98.4% Eff
Inelastic Tension:
Active
How to read: When a photon is injected at Node 1, its energy transforms into a delocalized exciton wave. It immediately samples all coupling bridges simultaneously. High coupling constant (J) values create wider, stiffer channels for instant transit.