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- Title
Infinite-Order Symmetries for Quantum Separable Systems.
- Authors
Miller, W.; Kalnins, E. G.; Kress, J. M.; Pogosyan, G. S.
- Abstract
We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schrödinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, we can develop a calculus for conformal symmetries of the time-dependent Schrödinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries.© 2005 Pleiades Publishing, Inc.
- Subjects
CALCULUS; DIFFERENTIAL operators; SYMMETRY; RIEMANNIAN manifolds; ORTHOGONAL arrays; PARAMETER estimation; PARALLEL algorithms
- Publication
Physics of Atomic Nuclei, 2005, Vol 68, Issue 10, p1756
- ISSN
1063-7788
- Publication type
Article
- DOI
10.1134/1.2121926