QCL Subband Eigenstates & Population-Inversion Dynamics (2D)

This is the same intersubband-transition physics as the 3D quantum-cascade-laser cascade view, but computed and rendered as two independent 2D-native panels instead of an animated staircase. A finite-difference Hamiltonian for the quantum well is diagonalized on-device with the Jacobi eigenvalue algorithm to obtain the confined-electron energy levels and their actual probability-density wavefunctions |ψ₁(x)|², |ψ₂(x)|² directly from numerical linear algebra — not the closed-form particle-in-a-box formula alone. Below it, the two-level rate equations governing population inversion are integrated forward in time with RK4 rather than solved instantly for their steady state, so a scrolling strip chart shows N₂(t), N₁(t) and ΔN(t) actually rising and settling whenever you move a slider, crossing (or falling short of) the lasing threshold in real time.