2019/12/17 by A. Carati, Carati, Andrea, L. Galgani +5
Physics and Astronomy · #Chemical Physics (physics.chem-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Applications #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1912.07933
openalex publication_date 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
According to the correspondence principle, classical mechanics and quantum mechanics agree in the semiclassical limit, although presently it has become more and more clear how intriguing would be to try to fix a boundary between them. Here we give a significant example in which the agreement concerns Newtonian trajectories of an electron with initial data corresponding to a quantum ground state. The example is the simplest case in which a chemical bond occurs, i.e. the H2+ ion. By molecular dynamics simulations for the full system (two protons and one electron) we show that there exist initial data producing an ``effective potential'' among the protons, which superposes in a surprisingly good way the quantum one computed in the Born-Oppenheimer approximation (Fig~1). Preliminarily, following the perturbation procedure first exhibited by Born and Heisenberg in the year 1924, we recall why an effective potential should exist in a classical frame, and also describe the numerical procedure employed in computing it.