Browsing by Author "Miller, Jr., W."
Now showing 1 - 20 of 23
Results Per Page
Sort Options
Item Complete sets of invariants for dynamical systems that admit a separation of variables(2002-02) Kalnins, E.G.; Kress, J.M.; Pogosyan, G.; Miller, Jr., W.Item Completeness of multiseparable superintegrability on the complex 2-sphere(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Item Completeness of mutiseparable superintegrability in E2, C(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Item Completeness of superintegrability in two dimensional constant curvature spaces(2000-12) Kalnins, E.G.; Kress, J.M.; Pogosyan, G.; Miller, Jr., W.We classify the Hamiltonians H=px2+ py2 +V(x,y) of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H=J12+J22+ J32+V(x,y,z) on the complex 2-sphere where x2+y2+z2=1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.Item Contractions of Lie algebras: Applications to special functions and separation of variables(1999-06) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Item Coulomb-oscillator duality in spaces of constant curvature(1998-12) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Item Coulomb-oscillator duality in spaces of constant curvature(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Item The Coulomb-oscillator relation on the N-sphere(1999-02) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Item Exact and quasi-exact solvability of second order superintegrable quantum systems. II. Relation to separation of variables(2006-12) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.S.Item Multiseparability and superintegrability for classical and quantum systems(1999-02) Miller, Jr., W.Item Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties(2006-12) Kalnins, E.G.; Kress, J.M.; Miller, Jr., W.Item A note on tensor products of q-algebra representations and orthogonal polynomials(1994-12) Kalnins, E.G.; Miller, Jr., W.Item On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space(2002-02) Kalnins, E.G.; Williams, G.C.; Miller, Jr., W.; Pogosyan, G.S.Item q-algebra representations of the Euclidean, pseudo-Euclidean and oscillator algebras, and their tensor products(1994-12) Kalnins, E.G.; Miller, Jr., W.Item q-Series and Orthogonal Polynomials Associated with Barnes' First Lemma(1987) Kalnins, E.G.; Miller, Jr., W.Item Quantum constants of the motion for two-dimensional systems(2003-03) Kalnins, E.G.; Miller, Jr., W.; Pogosyan, G.Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables then it is possible to generate algorithmically a canonical basis Q, P where P1 = H, P2, are the other 2nd-order constants of the motion associated with the separable coordinates, and [Qi, Qj] = [Pi, Pj] = 0, [Qi, Pj] = Deltaij. The 3 operators Q2, P1, P2 form a basis for the invariants. In general these are infinite-order differential operators. We shed some light on the general question of exactly when the Hamiltonian admits a constant of the motion that is polynomial in the momenta. We go further and consider all cases where the Hamilton-Jacobi equation admits a second-order constant of the motion, not necessarily associated with orthogonal separable coordinates, or even separable coordinates at all. In each of these cases we construct an additional constant of the motion.Item Separation of variables and the XXZ Gaudin magnet(1994-12) Kalnins, E.G.; Kuznetsov, V.B.; Miller, Jr., W.Item Separation of variables for the Dirac equation in Kerr Newman space time(1991-05) Kalnins, E.G.; Miller, Jr., W.Item Separation of Variables Methods for Systems of Differential Equations in Mathematical Physics(1989) Kalnins, E.G.; Miller, Jr., W.Item Special functions and perturbations of black holes(1999-02) Kalnins, E.G.; Miller, Jr., W.; Torres del Castillo, G.F.; Williams, G.C.