Quantum Superintegrable Systems in Flat Space: A Review
Analysis
This paper reviews six two-dimensional quantum superintegrable systems, confirming the Montreal conjecture. It highlights their exact solvability, algebraic structure, and polynomial algebras of integrals, emphasizing their importance in understanding quantum systems with special symmetries and their connection to hidden algebraic structures.
Key Takeaways
- •Reviews six 2D quantum superintegrable systems.
- •Confirms the Montreal conjecture.
- •Highlights exact solvability and algebraic properties.
- •Emphasizes the role of hidden algebraic structures.
Reference
“All models are exactly-solvable, admit algebraic forms for the Hamiltonian and integrals, have polynomial eigenfunctions, hidden algebraic structure, and possess a polynomial algebra of integrals.”