Visualization and dimensional scaling for some three-body problems in atomic and molecular quantum mechanics
- Department of Mathematics and Institute for Quantum Studies, Texas A and M University, College Station, Texas 77843 (United States)
- Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada 89154-4020 (United States)
- Laboratoire J.-L. Lions, Universite Pierre et Marie Curie, Paris Cedex 05 (France)
- Department of Mathematics, University of Houston, Houston, Texas 77004 (United States)
Three-body problems in atomic and molecular quantum mechanics, comprising one electron-two nuclei and two electron-one nucleus, are studied from their Schroedinger-Born-Oppenheimer models. The following are main topics of interest in this paper: (1) review of foundational mathematical properties of the multiparticle Schroedinger operator, (2) visualization of H{sub 2}{sup +} (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.
- OSTI ID:
- 21100312
- Journal Information:
- Journal of Mathematical Physics, Vol. 49, Issue 6; Other Information: DOI: 10.1063/1.2937002; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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