Infinite-order symmetries for quantum separable systems

W. Miller, E. G. Kalnins, J. M. Kress, G. S. Pogosyan

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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.

Original languageEnglish (US)
Pages (from-to)1756-1763
Number of pages8
JournalPhysics of Atomic Nuclei
Volume68
Issue number10
DOIs
StatePublished - Nov 7 2005

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    Miller, W., Kalnins, E. G., Kress, J. M., & Pogosyan, G. S. (2005). Infinite-order symmetries for quantum separable systems. Physics of Atomic Nuclei, 68(10), 1756-1763. https://doi.org/10.1134/1.2121926