Quasi-exactly solvable Schrödinger operators in three dimensions

DOI10.3842/SIGMA.2007.109zbMATH Open1136.81038arXiv0709.4528MaRDI QIDQ2473516

Publication date: 27 February 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Abstract: 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 Schr"odinger operators in three dimensions.

Full work available at URL: https://arxiv.org/abs/0709.4528

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zbMATH Keywords

Schrödinger operators quasi-exact solvability three dimensional manifolds Lie algebras of first order differential operators

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Exactly and quasi-solvable systems arising in quantum theory (81U15) Applications of global differential geometry to the sciences (53C80) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

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