  We present here the details of a method [A. B. Culver and N. Andrei, Phys.
Rev. B 103, L201103 (2021)] for calculating the time-dependent many-body
wavefunction that follows a local quench. We apply the method to the
voltage-driven nonequilibrium Kondo model to find the exact time-evolving
wavefunction following a quench where the dot is suddenly attached to the leads
at $t=0$. The method, which does not use Bethe ansatz, also works in other
quantum impurity models and may be of wider applicability. We show that the
long-time limit (with the system size taken to infinity first) of the
time-evolving wavefunction of the Kondo model is a current-carrying
nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We
show that the electric current in the time-evolving wavefunction is given by a
series expression that can be expanded either in weak coupling or in strong
coupling, converging to all orders in the steady-state limit in either case.
The series agrees to leading order with known results in the well-studied
regime of weak antiferromagnetic coupling and also reveals a universal regime
of strong ferromagnetic coupling with Kondo temperature $T_K^{(F)} = D
e^{-\frac{3\pi^2}{8} \rho |J|}$ ($J<0$, $\rho|J|\to\infty$). In this regime,
the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$
asymptotically at large voltage or temperature.
