Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics

Three-body problems in atomic and molecular quantum mechanics, comprising one electron–two nuclei and two electron–one nucleus, are studied from their Schrödinger–Born–Oppenheimer models. The following are main topics of interest in this paper: (1) review of foundational mathematical properties of the multiparticle Schrödinger operator, (2) visualization of H 2 + (hydrogen molecular ion)-like and He (helium)-like molecular and atomic states, and (3) spectrum of He obtained by the large-dimension scaling limit. The authors begin with topic (1) for the tutorial purpose and devote topics (2) and (3) to new contributions of the analytical, numerical, and visualization nature. Relevant heuristics, graphics, proofs, and calculations are presented.