The spatial derivative of nuclear density in quantum momentum results in coupled trajectories, which should be propagated simultaneously. The quantum momentum terms make CTMQC go beyond the traditional EMF dynamics and can naturally describe nuclear WP branching and decoherence. However, the accumulated errors in phases produce noisy potentials, which may make CTMQC numerically unstable. Inspired by the connection between EMF and SH dynamics, a direct alternative scheme arises: with the utilization of SH trajectories to sample nuclear configurations on adiabatic PESs, the numerical instability is expected to be circumvented. Following this idea, CTSH evolves the electronic wave function with Eq. ( ), but the trajectories now follow ( ) ( ) ( )