Integrable and superintegrable systems with spin in three-dimensional Euclidean space

A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spins 0 and is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one n...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2009-09, Vol.42 (38), p.385203-385203 (20)
Main Authors: Winternitz, Pavel, Yurduşen, İsmet
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spins 0 and is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one nontrivial example we show how superintegrability leads to exact solvability: we obtain exact (nonperturbative) bound-state energy formulas and exact expressions for the wave functions in terms of products of Laguerre and Jacobi polynomials.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/38/385203