The full time-dependent RealQM (complex Schrödinger, real time) evolved by a unitary Crank–Nicolson step with an absorbing edge — the same solver as the imaginary-time relaxation, only the time step changed. A metastable charge domain sits in a well behind a barrier and tunnels out. The trapped charge decays exponentially and a half-life emerges from the dynamics — no WKB, no fitting. Raise the barrier and the half-life grows (Geiger–Nuttall).
Left: |ψ(x)|² (blue) leaking through the barrier (grey). Right/below: trapped norm on a log axis — a straight line is exponential decay; the dashed line is the running fit whose slope gives the half-life. Well width a=5, barrier width w=1.5, m=ℏ=1.