In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.

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

Ciccotti G
2020

Abstract

In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.
2020
Istituto Applicazioni del Calcolo ''Mauro Picone''
INITIAL-VALUE REPRESENTATION; WAVE-PACKET DYNAMICS; SEMICLASSICAL DESCRIPTION; MOLECULAR-DYNAMICS; HYDRODYNAMIC EQUATIONS; SCHRODINGER-EQUATION; WAVEPACKET DYNAMICS; CLASSICAL DYNAMICS; TIME; EQUIDISTRIBUTION
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/384535
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