Alpha Decay Quantum Tunneling — 2D WKB Barrier Profile

This 2D companion to the 3D Gamow-theory simulator drops the camera fly-through and plots the underlying mathematics directly: the Coulomb barrier V(r), the alpha particle's fixed decay energy Q, and the cumulative WKB tunneling exponent building up across the classically-forbidden zone. A travelling marker crosses the barrier using genuine energy-conserving dynamics outside it and a κ(r)-throttled crawl inside it, then escapes or reflects at the turning point according to the real transmission probability. Two independently-coded integration methods for the Gamow exponent — a live pointwise trapezoid integral and an exact closed-form solution — are cross-checked against each other on every recompute, so the half-life you see is verified two different ways, not just asserted.