Classical trajectories: A powerful tool for solving tunneling problems

In the realm of Ehrenfest’s theorem, classical trajectories obeying Newton’s laws have been proven useful to construct explicit solutions to the time-dependent Wigner–Liouville equation. Whereas previous works have particularly focused on the initial distribution function as a vehicle found to carry the signatures of quantum statistics into the time-dependent solution, the present paper shows that the Lagrange–Charpit method based on classical trajectories can be successfully invoked as well to tackle quantum mechanical features with no classical counterpart, such as tunneling.