No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems
6. S. Y. Dubov, V. M. Eleonskii, and N. E. Kulagin, “Equidistant spectra of anharmonic oscillators,” Sov. Phys. JETP 75, 446 (1992).
10. J. F. Cariñena, A. M. Perelomov, M. F. Rañada, and M. Santander, “A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator,” J. Phys. A: Math. Theor. 41, 085301 (2008).
17. C.-L. Ho, “Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials,” Prog. Theor. Phys. 126, 185 (2011).
23. C.-L. Ho, “Prepotential approach to solvable rational extensions of harmonic oscillator and Morse potentials,” J. Math. Phys. 52, 122107 (2011).
26. P. Winternitz, Ya. A. Smorodinsky, M. Uhlir, and I. Fris, “Symmetry groups in classical and quantum mechanics,” Sov. J. Nucl. Phys. 4, 444 (1967).
27. E. G. Kalnins, J. M. Kress, W. Miller, Jr., and P. Winternitz, “Superintegrable systems in Darboux spaces,” J. Math. Phys. 44, 5811 (2003).
28. E. G. Kalnins, J. M. Kress, and W. Miller, Jr., “Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems,” J. Math. Phys. 47, 093501 (2006).
29. C. Daskaloyannis and K. Ypsilantis, “Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold,” J. Math. Phys. 47, 042904 (2006).
30. Á. Ballesteros, A. Enciso, F. J. Herranz, and O. Ragnisco, “Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles,” Ann. Phys. (N.Y.) 324, 1219 (2009).
31. S. Gravel and P. Winternitz, “Superintegrability with third-order invariants in quantum and classical mechanics,” J. Math. Phys. 43, 5902 (2002).
33. I. Marquette, “Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials,” J. Math. Phys. 50, 012101 (2009).
34. I. Marquette, “Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painlevé transcendent potentials,” J. Math. Phys. 50, 095202 (2009).
37. B. Demircioǧlu, Ş. Kuru, M. Önder, and A. Verçin, “Two families of superintegrable and isospectral potentials in two dimensions,” J. Math. Phys. 43, 2133 (2002).
38. I. Marquette, “Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion,” J. Math. Phys. 50, 122102 (2009).
40. I. Marquette and C. Quesne, “New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials,” J. Math. Phys. 54, 042102 (2013).
41. F. Cooper, A. Khare, and U. Sukhatme, Supersymmetry in Quantum Mechanics (World Scientific, Singapore, 2000).
42. I. Marquette and C. Quesne, “Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators,” J. Phys. A: Math. Theor. 46, 155201 (2013).
43. A. P. Veselov and A. B. Shabat, “Dressing chains and the spectral theory of the Schrödinger operator,” Funct. Anal. Appl. 27, 81 (1993).
Article metrics loading...
New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer m. The eigenstates of the Hamiltonian separate into m + 1 infinite-dimensional unitary irreducible representations of the corresponding polynomial Heisenberg algebra. These ladder operators are used to construct a higher-order integral of motion for two superintegrable two-dimensional systems separable in cartesian coordinates. The polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite-dimensional unitary irreducible representations.
Full text loading...
Most read this month