Willard Miller - Academia.edu (original) (raw)

Papers by Willard Miller

Research paper thumbnail of Symmetry and Separation of Variables: References

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Research paper thumbnail of Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties

Journal of Mathematical Physics, 2007

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 ...

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Research paper thumbnail of A new way to classify 2D higher order quantum superintegrable systems

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 ...

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Research paper thumbnail of Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates

Journal of Mathematical Physics, 1977

Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates. [Journal of Mathemat... more Lie theory and the wave equation in space–time. 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 ...

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Research paper thumbnail of Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré group

Journal of Mathematical Physics, 1978

Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré gro... more Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré group. [Journal of Mathematical Physics 19, 1233 (1978)]. EG Kalnins, W. Miller, Jr. Abstract. A detailed classification is made of ...

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Research paper thumbnail of Complete sets of invariants for dynamical systems that admit a separation of variables

Journal of Mathematical …, 2002

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 ...

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Research paper thumbnail of Lie theory and the wave equation in space–time. I. The Lorentz group

Journal of Mathematical Physics, 1977

Lie theory and the wave equation in space–time. I. The Lorentz group. [Journal of Mathematical Ph... more Lie theory and the wave equation in space–time. 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 ...

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Research paper thumbnail of Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries

Journal of mathematical physics, 2006

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 ...

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Research paper thumbnail of Superintegrability on the two-dimensional hyperboloid. II

Journal of Mathematical …, 1999

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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Research paper thumbnail of A New Approach to Analysis of 2D Higher Order Quantum Superintegrable Systems

Quantum Theory and Symmetries

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Research paper thumbnail of A new way to classify 2D higher order quantum superintegrable systems

Journal of Physics A: Mathematical and Theoretical

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Research paper thumbnail of Toward a classification of semidegenerate 3D superintegrable systems

Journal of Physics A: Mathematical and Theoretical

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Research paper thumbnail of R‐separation of variables for the time‐dependent Hamilton–Jacobi and Schrödinger equations

Journal of Mathematical Physics, 1987

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Research paper thumbnail of Complete sets of functions for perturbations of Robertson–Walker cosmologies and spin 1 equations in Robertson–Walker-type space-times

Journal of …, 1991

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Research paper thumbnail of Superintegrability and higher order integrals for quantum systems

Journal of Physics A: Mathematical …, 2010

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Research paper thumbnail of A Geometrical Perspective on the Coherent Multimode Optical Field and Mode Coupling Equations

IEEE Journal of Quantum Electronics, 2015

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Research paper thumbnail of Scientific Computation and Mathematical Modelling

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Research paper thumbnail of Separable components for three-dimensional complex riemannian spaces

Journal of Differential Geometry

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Research paper thumbnail of O a Class of Vector-Valued Functions Covariant Under the Classical Groups, with Applications to Physics

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Research paper thumbnail of Invariant Tensor Fields in Physics and the Classical Groups

Siamam, 1971

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Research paper thumbnail of Symmetry and Separation of Variables: References

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Research paper thumbnail of Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties

Journal of Mathematical Physics, 2007

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 ...

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Research paper thumbnail of A new way to classify 2D higher order quantum superintegrable systems

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 ...

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Research paper thumbnail of Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates

Journal of Mathematical Physics, 1977

Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates. [Journal of Mathemat... more Lie theory and the wave equation in space–time. 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 ...

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Research paper thumbnail of Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré group

Journal of Mathematical Physics, 1978

Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré gro... more Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré group. [Journal of Mathematical Physics 19, 1233 (1978)]. EG Kalnins, W. Miller, Jr. Abstract. A detailed classification is made of ...

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Research paper thumbnail of Complete sets of invariants for dynamical systems that admit a separation of variables

Journal of Mathematical …, 2002

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 ...

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Research paper thumbnail of Lie theory and the wave equation in space–time. I. The Lorentz group

Journal of Mathematical Physics, 1977

Lie theory and the wave equation in space–time. I. The Lorentz group. [Journal of Mathematical Ph... more Lie theory and the wave equation in space–time. 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 ...

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Research paper thumbnail of Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries

Journal of mathematical physics, 2006

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 ...

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Research paper thumbnail of Superintegrability on the two-dimensional hyperboloid. II

Journal of Mathematical …, 1999

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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Research paper thumbnail of A New Approach to Analysis of 2D Higher Order Quantum Superintegrable Systems

Quantum Theory and Symmetries

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Research paper thumbnail of A new way to classify 2D higher order quantum superintegrable systems

Journal of Physics A: Mathematical and Theoretical

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Research paper thumbnail of Toward a classification of semidegenerate 3D superintegrable systems

Journal of Physics A: Mathematical and Theoretical

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Research paper thumbnail of R‐separation of variables for the time‐dependent Hamilton–Jacobi and Schrödinger equations

Journal of Mathematical Physics, 1987

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Research paper thumbnail of Complete sets of functions for perturbations of Robertson–Walker cosmologies and spin 1 equations in Robertson–Walker-type space-times

Journal of …, 1991

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Research paper thumbnail of Superintegrability and higher order integrals for quantum systems

Journal of Physics A: Mathematical …, 2010

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Geometrical Perspective on the Coherent Multimode Optical Field and Mode Coupling Equations

IEEE Journal of Quantum Electronics, 2015

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Research paper thumbnail of Scientific Computation and Mathematical Modelling

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Separable components for three-dimensional complex riemannian spaces

Journal of Differential Geometry

Bookmarks Related papers MentionsView impact

Research paper thumbnail of O a Class of Vector-Valued Functions Covariant Under the Classical Groups, with Applications to Physics

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Invariant Tensor Fields in Physics and the Classical Groups

Siamam, 1971

Bookmarks Related papers MentionsView impact