2008/12/23 by Anders Szepessy, Szepessy, Anders
Mathematics · Physics and Astronomy · #81Q20 #82C10 #82C31 #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP #msc:81Q20 #msc:82C10 #msc:82C31
paper · pdf · doi:10.48550/arxiv.0812.4338
36 pages: improved convergence rates for Ehrenfest observables with crossing eigenvalues and corrected estimates for wave functions approximating electron eigenstates; stability proved for crossing electron eigenvalues, temperature dependent drift correction included
openalex publication_date 2008/12/23 · arxiv created 2010/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schrödinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schrödinger equation and stability of the corresponding Hamilton-Jacobi equation, bypasses the usual separation of nuclei and electron wave functions, includes crossing electron eigenvalues, and gives a different perspective on the Born-Oppenheimer approximation, Schrödinger Hamiltonian systems, stochastic electron equilibrium states and numerical simulation in molecular dynamics modeling.