where |Ψ i ⟩ is the ket at a certain nuclear time step for the i th trajectory, and similarly, for the propagation of backward coefficients, we can make a batch matrix {⟨Ψ|} m by collecting ⟨Ψ i | from "m" different trajectories. Similarly, we can also bunch together the diagonal energy fluctuations from these trajectories as columns of a batch matrix {ϵ} m , of size K × m,