Polynomial Associative Algebras for Quantum Superintegrable Systems with a Third Order Integral of Motion

Details Polynomial Associative Algebras for Quantum Superintegrable Systems with a Third Order Integral of Motion Polynomial Associative Algebras for Quantum Superintegrable Systems with a Third Order Integral of Motion

2007-01-26

arxiv.org/abs/math-ph/0701065v1

Symmetries and Overdetermined Systems of Partial Differential Equations,The IMA Volumes in Mathematics and its Applications, S

Physics

Mathematical Physics

Scientific paper

10.1063/1.2831929

We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in cartesian coordinates with a third order integral are known. The general formalism is applied to one of the quantum potentials.

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