The exact factorization formalism is an overarching strategy in quantum mechanics that is closely related to probability theory. It allows to express the given Schrödinger equation into two coupled equations by writing the wavefunction as a product of a marginal and conditional amplitude. Initially proposed as a way to tackle the full electron-nuclear problem beyond the Born-Oppenheimer approximation in a static setting , the exact factorization has later been extended to the time-dependent one , proving considerably successful as a trajectory-based method for ab initio molecular dynamics .