On a Generalized Kepler-Coulomb System: Interbasis Expansions
نویسنده
چکیده
This paper deals with a dynamical system that generalizes the Kepler-Coulomb system and the Hartmann system. It is shown that the Schrödinger equation for this generalized KeplerCoulomb system can be separated in prolate spheroidal coordinates. The coefficients of the interbasis expansions between three bases (spherical, parabolic and spheroidal) are studied in detail. It is found that the coefficients for the expansion of the parabolic basis in terms of the spherical basis, and vice-versa, can be expressed through the Clebsch-Gordan coefficients for the group SU(2) analytically continued to real values of their arguments. The coefficients for the expansions of the spheroidal basis in terms of the spherical and parabolic bases are proved to satisfy three-term recursion relations.
منابع مشابه
ua nt - p h / 97 12 01 4 v 1 5 D ec 1 99 7 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 continuat...
متن کاملMaximal superintegrability of the generalized Kepler–Coulomb system on N-dimensional curved spaces
The superposition of the Kepler–Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable [Verrier P E and Evans N W 2008 J. Math. Phys. 49 022902] by finding an additional (hidden) integral of motion which is quartic in the momenta. In this paper we present the generalization of this result to the ND spherical, hyperbolic a...
متن کاملSpectral action for a one-parameter family of Dirac operators on SU(2) and SU(3)
Related Articles Instantons on the six-sphere and twistors J. Math. Phys. 53, 123506 (2012) Generalized Runge-Lenz vector and a hidden symmetry of the nine-dimensional MICZ-Kepler problem J. Math. Phys. 53, 082103 (2012) Topological aspects of fermions on hyperdiamond J. Math. Phys. 53, 072304 (2012) Generalized five-dimensional Kepler system, Yang-Coulomb monopole, and Hurwitz transformation J...
متن کاملStructure Theory for Extended Kepler–coulomb 3d Quantum Superintegrable Systems
A quantum superintegrable system is an integrable n-dimensional Hamiltonian system with potential: H = ∆n + V that admits 2n − 1 algebraically independent partial differential operators commuting with the Hamiltonian, the maximum number possible. The system is of order ` if the maximum order of the symmetry operators, other than H, is `. Typically, the algebra generated by the symmetry operator...
متن کاملUnfamiliar trajectories for a relativistic particle in a Kepler or Coulomb potential V ( r ) = − α / r
Abstract Relativistic particles in the Kepler and Coulomb potentials may have trajectories that are qualitatively different from the trajectories found in nonrelativistic mechanics. Spiral scattering trajectories were pointed out by C. G. Darwin in 1913 in connection with the relativistic Rutherford scattering of classical charged particles. Relativistic trajectories are of current interest in ...
متن کامل