An exact solution of a ring-shaped oscillator plus a potential

Path integral formulations for the Smorodinsky‐Winternitz potentials in two‐ and three‐dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky‐Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave‐functions.

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“…For F (y/x) = γ 2 > 0 this potential is known as the ring-shaped Hartmann potential (c.f. Calogero [9], Carpio-Bernido et al [10,11,13,12]…”

Section: 34mentioning

confidence: 99%

Path Integral Discussion for Smorodinsky-Winternitz Potentials: I. Two- and Three Dimensional Euclidean Space

1995

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“…The study of exact solutions of the nonrelativistic equation for a class of non-central potentials with a vector potential and a non-central scalar potential is of considerable interest in quantum chemistry [31][32][33][34][35][36][37]. In recent years, numerous studies [38][39][40] have been made in analyzing the bound states of an electron in a Coulomb field with simultaneous presence of Aharonov-Bohm (AB) [41] field, and/or a magnetic Dirac monopole [42], and AharonovBohm plus oscillator (ABO) systems.…”

Section: Introductionmentioning

confidence: 99%

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Ikhdair¹,

Sever

2008

Open Physics

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“…This potential has been treated, within the circular cylinder coordinates, through the resolution of Schrödinger's equation [4], and via the path integral approach [32]. The parameters (26) and (33) can thus written…”

Section: First Case the Ring-shaped Oscillatormentioning

confidence: 99%

Path integral treatment of a noncentral electric potential

et al. 2013

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Abstract:We present a rigorous path integral treatment of a dynamical system in the axially symmetric potentialIt is shown that the Green's function can be calculated in spherical coordinate system for V (θ) = . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number ≥ 0, are recovered.

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An exact solution of a ring-shaped oscillator plus a potential

Cited by 51 publications

References 11 publications

Path Integral Discussion for Smorodinsky-Winternitz Potentials: I. Two- and Three Dimensional Euclidean Space

Path Integral Discussion for Smorodinsky-Winternitz Potentials: I. Two- and Three Dimensional Euclidean Space

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Path integral treatment of a noncentral electric potential

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