The ₂ Harmonic Oscillator with Reflections and Superintegrability

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Author: Dunkl, Charles F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211918
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The ₂ Harmonic Oscillator with Reflections and Superintegrability. Charles F. Dunkl. SIGMA 19 (2023), 025, 18 pages

The two-dimensional quantum harmonic oscillator is modified with reflection terms associated with the action of the Coxeter group ₂, which is the symmetry group of the square. The angular momentum operator is also modified with reflections. The wavefunctions are known to be built up from Jacobi and...