Journal ArticleDOI
Motion of a particle in a ring-shaped potential: an approach via a nonbijective canonical transformation
Maurice R. Kibler,Tidjani Négadi +1 more
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TLDR
In this paper, the problem of a particle in the three-dimensional ring-shaped potential ησ2(2a0/r − ηa/r2 sin2 θ)e0 introduced by Hartmann is transformed into a coupled pair two-dimensional harmonic oscillators with inverse quadratic potentials by using a non-bijective canonical transformation, viz., the Kustaanheimo-Stiefel transformation.Abstract:
The problem of a particle in the three-dimensional ring-shaped potential ησ2(2a0/r − ηa/r2 sin2 θ)e0 introduced by Hartmann is transformed into the problem of a coupled pair two-dimensional harmonic oscillators with inverse quadratic potentials by using a nonbijective canonical transformation, viz., the Kustaanheimo–Stiefel transformation. The energy E of the levels for the ring-shaped potential is obtained in a straightforward way from the one for the two-dimensional potential — (4Eρ2 + η2σ2a e0/ρ2).read more
Citations
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Path Integral Discussion for Smorodinsky‐Winternitz Potentials: I. Two‐ and Three Dimensional Euclidean Space
TL;DR: In this paper, path integral formulations for the Smorodinsky-Winternitz potentials in two-and three-dimensional Euclidean space are presented, where path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave-functions are discussed.
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Exactly complete solutions of the Schrödinger equation with a spherically harmonic oscillatory ring-shaped potential
TL;DR: In this article, a spherically harmonic oscillatory ring-shaped potential is proposed and its exactly complete solutions are presented by the Nikiforov-Uvarov method.
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Dynamical invariance algebra of the Hartmann potential
TL;DR: In this article, a dynamical invariance algebra is constructed for the ring-shaped potential V = eta sigma 2r-1+1/2q eta 2sigma 2(r sin theta )-2.
Journal ArticleDOI
Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential
Chang Yuan Chen,Shi-Hai Dong +1 more
TL;DR: In this article, a ring-shaped potential was proposed to solve the Schrodinger equation with the bound states and the exact solutions of the continuous states of the quantum system were derived.
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Exact solutions of the modified kratzer potential plus ring-shaped potential in the d-dimensional schrödinger equation by the nikiforov–uvarov method
Sameer M. Ikhdair,Ramazan Sever +1 more
TL;DR: In this paper, the exact energy bound-states solutions of the Schrodinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov-Uvarov method were obtained.
References
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Journal ArticleDOI
Perturbation theory of Kepler motion based on spinor regularization.
E. Stiefel,P. Kustaanheimo +1 more
TL;DR: In this article, Kustaanheimo et al. developed a regularization of Kepler motion using a simple mapping of a four-dimensional space R* onto a 3D space Ä, where the equations of any undisturbed Kepler motion are linear differential equations.
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Die Bewegung eines Körpers in einem ringförmigen Potentialfeld
TL;DR: In this article, a quantenmechanische Problem eines Teilchens in einem ringformigen potential der art is studied, i.e., the problem of quantifying the quantification of a Teilchen in a ring formigen potential of the art.
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Spin–orbit coupling for the motion of a particle in a ring‐shaped potential
Hermann Hartmann,Dieter Schuch +1 more
TL;DR: In this article, the Schrodinger equation for a particle in the ring-shaped potential V(r,v) = ησ2(2a0/r−a/r2 sin2v)e0, defined in the whole space, was solved exactly.
Journal ArticleDOI
Quantum theory of infinite component fields
TL;DR: In this paper, the quantum theory of the infinite component SO(4,2) fields is formulated as a model for relativistic composite objects, and three classes of physical solutions to a general class of infinite component wave equations are discussed.
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On the connection between the hydrogen atom and the harmonic oscillator
Maurice R. Kibler,Tidjani Négadi +1 more
TL;DR: The connection between a three-dimensional hydrogen-like atom and a pair of coupled two-dimensional harmonic oscillators was established by applying the Jordan-Schwinger boson calculus to the algebra of the Runge-Lenz-Laplace-Pauli vector as discussed by the authors.