Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test

Area of Science:

• Quantum mechanics
• Theoretical chemistry
• Computational physics

Background:

• The exact factorization method separates electron and nuclear motion.
• Solving the nuclear time-dependent Schrödinger equation (TDSE) is computationally challenging.
• Quantum trajectories offer a potential alternative to traditional wave function propagation.

Purpose of the Study:

• To investigate solving the nuclear TDSE using trajectories.
• To implement a method for following nuclear density evolution along quantum trajectories.
• To assess the feasibility of reconstructing the nuclear wave function via this approach.

Main Methods:

• Exact factorization of the electron-nuclear wave function.
• Separation of the nuclear TDSE into Hamilton-Jacobi and continuity equations.
• Propagation of nuclear density along characteristics (quantum trajectories) of the Hamilton-Jacobi equation.

Main Results:

• Demonstrated a procedure to follow nuclear density evolution along quantum trajectories for 1D models.
• Showcased that quantum trajectories, including a quantum potential, can reconstruct the nuclear wave function.
• Confirmed the method's applicability for both adiabatic and non-adiabatic systems.

Conclusions:

• Quantum trajectories provide a viable framework for solving the nuclear TDSE.
• The Hamilton-Jacobi equation's characteristics offer a path to understanding nuclear dynamics.
• Exact reconstruction of the wave function is achievable with sufficient initial conditions.