LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Marquette, Ian (2013)
Languages: English
Types: Preprint
Subjects: Mathematical Physics
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog and we extend Daskaloyannis' construction in obtained in context of quadratic algebras and we obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite dimensional unitary irreductible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptionnal orthogonal polynomials introduced recently.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] Zhedanov A. S., Hidden Symmetry of Askey-Wilson Polynomials, Theor and Math. Phys. 89 2 (1991) 1146-1157
    • [2] Granovsky Ya.A, Zhedanov A.S. and Lutzenko I.M., Quadratic algebra as a ”hidden” symmetry of the Hartmann potential, J.Phys.A:Math.Gen. 4 3887-3894 (1991)
    • [3] Granovskii Ya.I., Zhedanov A.S. and Lutzenko I.M., Quadratic algebras and dynamics in curved spaces. II. The Kepler problem Theoret. and Math. Phys. 89 (1992) 474-480, Theoret. and Math. Phys. 91 (1992) 604-612
    • [4] Granovskii Ya.I., Lutzenko I.M., Zhedanov A.S., Mutual integrability, quadratic algebras, and dynamical symmetry, Ann. Physics 217 (1992), 1-20.
    • [5] Granovskii Ya.I., Zhedanov A.S., Lutsenko I.M., Quadratic algebras and dynamics in curved space. I. Oscillator, Theoret. and Math. Phys. 91 (1992), 474-480.
    • [6] Zhedanov A.S., Hidden symmetry algebra and overlap coefficients for two ring-shaped potentials, J.Phys.A.:Math.gen. 26 4633-4641 (1993)
    • [7] Bonatsos D., Daskaloyannis C. and Kokkotas K., Quantum-algebraic description of quantum superintegrable systems in two dimensions, Phys.Rev. A 48 (1993) R3407-R3410
    • [8] Bonatsos D., Daskaloyannis C. and Kokkotas K., Deformed oscillator algebras for two-dimensional quantum superintegrable systems, Phys. Rev. A 50 (1994) 3700-3709
  • No related research data.
  • No similar publications.

Share - Bookmark

Funded by projects

Cite this article

Collected from