  We consider nonadiabatic systems in which the classical Born-Oppenheimer
approximation breaks down. We present a general theory that accurately captures
the full transmitted wavepacket after multiple transitions through either a
single or distinct avoided crossings, including phase information and
associated interference effects. Under suitable approximations, we recover both
the celebrated Landau-Zener formula and standard surface-hopping algorithms.
Our algorithm shows excellent agreement with the full quantum dynamics for a
range of avoided crossing systems, and can also be applied to single full
crossings with similar accuracy.
