Fortin Boisvert, Mélisande Quasi-exactly solvable Schrödinger operators in three dimensions. (English) Zbl 1136.81038 SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 109, 24 p. (2007). Summary: The main contribution of our paper is to give a partial classification of the quasi-exactly solvable Lie algebras of first order differential operators in three variables, and to show how this can be applied to the construction of new quasi-exactly solvable Schrödinger operators in three dimensions. MSC: 81U15 Exactly and quasi-solvable systems arising in quantum theory 81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory 22E70 Applications of Lie groups to the sciences; explicit representations 53C80 Applications of global differential geometry to the sciences Keywords:quasi-exact solvability; Schrödinger operators; Lie algebras of first order differential operators; three dimensional manifolds PDFBibTeX XMLCite \textit{M. Fortin Boisvert}, SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 109, 24 p. (2007; Zbl 1136.81038) Full Text: DOI arXiv EuDML EMIS