Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties... more Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties. [Journal of Mathematical Physics 48, 113518 (2007)]. EG Kalnins, JM Kress, W. Miller, Jr. Abstract. A classical (or quantum ...
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symm... more We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schrödinger eigenvalue equation HΨ≡ (Δ_2 +V)Ψ=EΨ on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal coordinate system. We apply the method, as an example, to revisit the Tremblay and Winternitz (2010) derivation of the Painlevé VI potential for a 3rd order superintegrable flat space system that separates in polar coordinates and, as new results, we give a listing of the possible potentials on the 2-sphere that separate in spherical coordinates and 2-hyperbolic (two-sheet) potentials separating in horocyclic coordinates. In particular, we show that the Painlevé VI potential also appears for a 3rd order superintegrable system on the 2-sphere that separates in spherical coordinates, as well as a 3rd order superintegrable system on the 2-hyperboloid that separates in spherical coordinates and one ...
Lie theory and the wave equation in spacetime. 3. Semisubgroup coordinates. [Journal of Mathemat... more Lie theory and the wave equation in spacetime. 3. Semisubgroup coordinates. [Journal of Mathematical Physics 18, 271 (1977)]. EG Kalnins, W. Miller, Jr. Abstract. We classify and study those coordinate systems which permit ...
Lie theory and the wave equation in spacetime. 4. The KleinGordon equation and the Poincaré gro... more Lie theory and the wave equation in spacetime. 4. The KleinGordon equation and the Poincaré group. [Journal of Mathematical Physics 19, 1233 (1978)]. EG Kalnins, W. Miller, Jr. Abstract. A detailed classification is made of ...
Complete sets of invariants for dynamical systems that admit a separation of variables. [Journal ... more Complete sets of invariants for dynamical systems that admit a separation of variables. [Journal of Mathematical Physics 43, 3592 (2002)]. EG Kalnins, JM Kress, W. Miller, Jr., GS Pogosyan. Abstract. Consider a classical Hamiltonian ...
Lie theory and the wave equation in spacetime. I. The Lorentz group. [Journal of Mathematical Ph... more Lie theory and the wave equation in spacetime. I. The Lorentz group. [Journal of Mathematical Physics 18, 1 (1977)]. EG Kalnins, W. Miller, Jr. Abstract. In this article we begin a study of the relationship between separation of ...
Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean sp... more Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries. [Journal of Mathematical Physics 47, 033502 (2006)]. EG Kalnins, W. Miller, Jr., GS Pogosyan. Abstract. We ...
Superintegrability on the two-dimensional hyperboloid. II. [Journal of Mathematical Physics 40, 2... more Superintegrability on the two-dimensional hyperboloid. II. [Journal of Mathematical Physics 40, 2291 (1999)]. EG Kalnins, W. Miller, Jr., Ye. M. Hakobyan, GS Pogosyan. Abstract. This work is devoted to the investigation of the quantum ...
Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties... more Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties. [Journal of Mathematical Physics 48, 113518 (2007)]. EG Kalnins, JM Kress, W. Miller, Jr. Abstract. A classical (or quantum ...
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symm... more We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schrödinger eigenvalue equation HΨ≡ (Δ_2 +V)Ψ=EΨ on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal coordinate system. We apply the method, as an example, to revisit the Tremblay and Winternitz (2010) derivation of the Painlevé VI potential for a 3rd order superintegrable flat space system that separates in polar coordinates and, as new results, we give a listing of the possible potentials on the 2-sphere that separate in spherical coordinates and 2-hyperbolic (two-sheet) potentials separating in horocyclic coordinates. In particular, we show that the Painlevé VI potential also appears for a 3rd order superintegrable system on the 2-sphere that separates in spherical coordinates, as well as a 3rd order superintegrable system on the 2-hyperboloid that separates in spherical coordinates and one ...
Lie theory and the wave equation in spacetime. 3. Semisubgroup coordinates. [Journal of Mathemat... more Lie theory and the wave equation in spacetime. 3. Semisubgroup coordinates. [Journal of Mathematical Physics 18, 271 (1977)]. EG Kalnins, W. Miller, Jr. Abstract. We classify and study those coordinate systems which permit ...
Lie theory and the wave equation in spacetime. 4. The KleinGordon equation and the Poincaré gro... more Lie theory and the wave equation in spacetime. 4. The KleinGordon equation and the Poincaré group. [Journal of Mathematical Physics 19, 1233 (1978)]. EG Kalnins, W. Miller, Jr. Abstract. A detailed classification is made of ...
Complete sets of invariants for dynamical systems that admit a separation of variables. [Journal ... more Complete sets of invariants for dynamical systems that admit a separation of variables. [Journal of Mathematical Physics 43, 3592 (2002)]. EG Kalnins, JM Kress, W. Miller, Jr., GS Pogosyan. Abstract. Consider a classical Hamiltonian ...
Lie theory and the wave equation in spacetime. I. The Lorentz group. [Journal of Mathematical Ph... more Lie theory and the wave equation in spacetime. I. The Lorentz group. [Journal of Mathematical Physics 18, 1 (1977)]. EG Kalnins, W. Miller, Jr. Abstract. In this article we begin a study of the relationship between separation of ...
Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean sp... more Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries. [Journal of Mathematical Physics 47, 033502 (2006)]. EG Kalnins, W. Miller, Jr., GS Pogosyan. Abstract. We ...
Superintegrability on the two-dimensional hyperboloid. II. [Journal of Mathematical Physics 40, 2... more Superintegrability on the two-dimensional hyperboloid. II. [Journal of Mathematical Physics 40, 2291 (1999)]. EG Kalnins, W. Miller, Jr., Ye. M. Hakobyan, GS Pogosyan. Abstract. This work is devoted to the investigation of the quantum ...
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