In SH dynamics, this can be realized by collapsing the wave function to its active state. In CTMQC, the concept of active states does not exist, and no inconsistency occurs as the WP is split by the quantum momentum with the electronic wave function collapsing to the corresponding state (see Figure ). In SHXF, since the trajectory on the lower (upper) PES moves faster (slower) than its auxiliary trajectory on the upper (lower) PES, the decoherence term correctly collapses the wave function to the active state and makes the active state and electronic coefficients consistent (see Figure ). In CTSH, however, as the quantum momentum splits both WPs on the upper and lower PESs and should cause opposite decoherence effects to these two parts, the wave function of trajectories belonging to one of the two parts is inconsistent with the active state (see Figure ). To achieve a consistent decoherence scheme in CTSH, we here consider a sign correction factor ( ) ( ) I t λ , which modifies the decoherence term to make the electronic wave functions match the active states (see Figure ). In detail, we multiply the decoherence term related to the quantum momentum by ( ) ( )