Infinite-order symmetries for quantum separable systems

We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calculus exhibits structure not apparent when one studi...

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Bibliographic Details
Published inPhysics of atomic nuclei Vol. 68; no. 10; pp. 1756 - 1763
Main Authors Miller, W., Kalnins, E. G., Kress, J. M., Pogosyan, G. S.
Format Journal Article
LanguageEnglish
Published United States 01.10.2005
Subjects
CONFORMAL INVARIANCE
COORDINATES
EIGENFUNCTIONS
EIGENVALUES
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POLYNOMIALS
RIEMANN SPACE
SCHROEDINGER EQUATION
SYMMETRY
TIME DEPENDENCE
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Summary:We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger 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 Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries.
ISSN:1063-7788
1562-692X
DOI:10.1134/1.2121926