Exact solvability of superintegrable systems

By P. Tempesta, A. Turbiner, P. Winternitz. 2000

150 citations recorded by the source corpus.

It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra sl(3). The gauge-rotated Hamiltonians, as well as their integrals of motion, once rewritten in appropriate coordinates, preserve a flag of polynomials. This flag corresponds to highest-weight finite-dimensional representations of the sl(3)-algebra, realized by first-order differential operators.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4ca90e57244670fe4e369b9a1e320ca87ac3433c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. P. Winternitz
2. Sarah Post
3. Willard Miller Jr.

In Statistical and Nonlinear Physics

1. P. Winternitz
2. Sarah Post
3. Willard Miller Jr.

Citations in the corpus

• Classical and quantum superintegrability with applications (2013, background): “It has been conjectured that all maximally superintegrable Euclidean systems are exactly solvable, thus it should always apply for these systems [178].”