Die Bewegung eines K�rpers in einem ringf�rmigen Potentialfeld

The separability and Runge-Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonović et al. [1], is traced back to that of the perturbed Kepler problem. A large class of axially symmetric perturbing potentials which allow for separation in parabolic coordinates can easily be found. Apart of the 2:1 anisotropic harmonic trapping potential considered in [1], they include a constant electric field parallel to the magnetic field (Stark effect), the ring-shaped Hartmann potential, etc. The harmonic case is studied in detail.

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“…[17,18]. The spherical Stäckel quantities are (2.10) except for the last contribution to w which, fixed by the potential,…”

Section: Further Separable Perturbationsmentioning

confidence: 99%

Separability and dynamical symmetry of Quantum Dots

et al. 2014

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“…It is straight forward to check that this non-Hermitian system is PT symmetric, where in 3-d in spherical polar coordinates the parity transformation is defined as, r → r; θ → π − θ , φ → φ + 2π.This particular potential is very important as the Coulomb and the ring-shaped potentials are particular cases of this potential. For C = 0 this potential becomes Hartman's ring shaped potential which was originally proposed to model Benzene molecule [14]. To proceed with this Hamiltonian we first consider the most general Hamiltonian of Liouville type written as…”

Section: Green's Functions For the Pt-symmetric Non-central Potentialmentioning

confidence: 99%

Green’s Function of a General PT-Symmetric Non-Hermitian Non-central Potential

Mourya

Mandal

2016

Springer Proceedings in Physics

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We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamiltonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green's functions for a general non-central PT symmetric non hermitian potential are calculated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time .

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“…There are some noncentral separable potentials in spherical coordinates which are of considerable interest and are practical in the branches of science such as chemistry and nuclear physics. Hartmann potential introduced by Hartmann is one of the noncentral potentials, which can be realized by adding a potential proportional to Coulomb potential [11][12][13][14][15][16]. This potential was suggested to describe the energy spectrum of Ring-Shaped Potential obtained by replacing the Coulomb part of Hartmann potential with a Harmonic Oscillator term and that is called a Ring-Shaped Oscillator Potential, which is investigated to find discrete spectrum and integrals of motions [17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials

Bakhshi

2018

Advances in High Energy Physics

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The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrödinger-like equation obtained by Dirac equation with the nonrelativistic solvable models is the most efficient method. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped Oscillator Potentials are accessible, when the scalar potential is equal to the vector potential. Using solvable nonrelativistic quantum mechanics systems as a basic model and considering the physical conditions provide the changes in the restrictions of relativistic parameters based on the nonrelativistic definitions of parameters.

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Die Bewegung eines K�rpers in einem ringf�rmigen Potentialfeld

Cited by 174 publications

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Separability and dynamical symmetry of Quantum Dots

Separability and dynamical symmetry of Quantum Dots

Green’s Function of a General PT-Symmetric Non-Hermitian Non-central Potential

Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials

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