https://hal-cnrs.archives-ouvertes.fr/hal-03217883Jecko, ThierryThierryJeckoAGM - UMR 8088 - Analyse, Géométrie et Modélisation - CNRS - Centre National de la Recherche Scientifique - CY - CY Cergy Paris UniversitéSutcliffe, BrianBrianSutcliffeULB - Université libre de BruxellesWoolley, RRWoolleyOn Factorization of Molecular WavefunctionsHAL CCSD2015[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph][MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Jecko, Thierry2021-05-05 10:45:072023-02-07 14:45:142021-05-11 08:39:54enJournal articleshttps://hal-cnrs.archives-ouvertes.fr/hal-03217883/document10.1088/1751-8113/48/44/445201application/pdf1Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions {Φ} of the molecular Schrödinger equation as originally proposed by Hunter in the 1970s. The idea is to represent Φ in the form ϕχ where χ is purely a function of the nuclear coordinates, while ϕ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an 'exact' representation of Φ can be achieved in this form with ϕ and χ interpretable as 'electronic' and 'nuclear' wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.An erratum is available here and published in J. Phys. A: Math. Theor. 51, 2018, 149501.