Landau-Zener Avoided Crossing: Exact Two-Level Solver

This is the 2D companion to the adiabatic quantum optimization simulator. Where the 3D version tracks a many-body ground state through an N-spin Ising Hamiltonian, this simulator isolates the single physical mechanism behind every avoided crossing — the exactly solvable Landau-Zener two-level model — and integrates the real time-dependent Schrodinger equation for it via RK4, live, in the browser. The energy panel plots the diabatic and adiabatic branches as the sweep parameter advances through the avoided crossing; the population panel traces the numerically computed probability of remaining in the original diabatic state against the closed-form Landau-Zener transition probability P_LZ = exp(−πC²/v), so you can watch the exact formula and the independent numeric integration agree in real time as you change the coupling strength and sweep rate.