379 research outputs found
On a Generalized Oscillator System: Interbasis Expansions
This article deals with a nonrelativistic quantum mechanical study of a
dynamical system which generalizes the isotropic harmonic oscillator system in
three dimensions. The problem of interbasis expansions of the wavefunctions is
completely solved. A connection between the generalized oscillator system
(projected on the z-line) and the Morse system (in one dimension) is discussed.Comment: 23 pages, Latex File, to be published in International Journal of
Quantum Chemistr
Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions
In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator
Coulomb-oscillator duality in spaces of constant curvature
In this paper we construct generalizations to spheres of the well known
Levi-Civita, Kustaanheimo-Steifel and Hurwitz regularizing transformations in
Euclidean spaces of dimensions 2, 3 and 5. The corresponding classical and
quantum mechanical analogues of the Kepler-Coulomb problem on these spheres are
discussed.Comment: 33 pages, LaTeX fil
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