2,206 research outputs found
Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics
We investigate dynamics of probe particles moving in the near-horizon limit
of (2N+1)-dimensional extremal Myers-Perry black hole with arbitrary rotation
parameters. We observe that in the most general case with nonequal nonvanishing
rotational parameters the system admits separation of variables in
N-dimensional ellipsoidal coordinates. This allows us to find solution of the
corresponding Hamilton-Jacobi equation and write down the explicit expressions
of Liouville constants of motion.Comment: 9 pages, no figures, v2: Minor changes to match the published versio
On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions
This article deals with a quantum-mechanical system which generalizes the
ordinary isotropic harmonic oscillator system. We give the coefficients
connecting the polar and Cartesian bases for D=2 and the coefficients
connecting the Cartesian and cylindrical bases as well as the cylindrical and
spherical bases for D=3. These interbasis expansion coefficients are found to
be analytic continuations to real values of their arguments of the
Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable
character for the generalized oscillator system is investigated from the points
of view of a quadratic invariance algebra.Comment: 13 pages, Latex file. Submitted for publication to Yadernaya Fizik
Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries
We show that second-order superintegrable systems in two-dimensional and three-dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separation of variables, and demonstrate the increased insight into the structure of such problems provided by superintegrability. A principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable. Most past separation of variables treatments of QES problems via partial differential equations have only incorporated separability, not multiseparability. Also, we propose another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schrödinger equation can be expressed in terms of hypergeometric functions mFn and is QES if the Schrödinger equation admits polynomial solutions with coefficients necessarily satisfying a three-term or higher order of recurrence relations. In three dimensions we give an example of a system that is QES in one set of separable coordinates, but is not ES in any other separable coordinates. This example encompasses Ushveridze's tenth-order polynomial QES problem in one set of separable coordinates and also leads to a fourth-order polynomial QES problem in another separable coordinate set
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