Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton–Jacobi formalism

Gharbi, Abdelhakim; Bouda, A.

doi:10.1088/0031-8949/88/04/045007

Cited by 8 publications

(12 citation statements)

References 29 publications

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“…The study of non-central potentials began with the pioneering works of Makarov [1] and Hartman [2], and was then properly structured with the work of Hautot [3]. Their results paved the way for realistic applications of non-central-potential problems such as ring-shaped organic molecules which include, for instance, cyclic polyenes and benzene [4]. Since then there has been a significant interest in the literature in studies of non-central and ring-shaped potentials (see for instance…”

Section: Introductionmentioning

confidence: 99%

Schrödinger equation for non-pure dipole potential in 2D systems

Moumni

Falek

2016

Journal of Mathematical Physics

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In this work, we analytically study the Schrödinger equation for the (non-pure) dipolar ion potential V (r) = q/r + D cos θ/r 2 , in the case of 2D systems using the separation of variables and the Mathieu equations for the angular part. We give the expressions of eigenenergies and eigenfunctions and study their dependence on the dipole moment D. Imposing the condition of reality on the energies E n,m implies that the dipole moment must not exceed a maximum value otherwise the corresponding bound state disappears.We also find that the s states (m = 0) can no longer exist in the system as soon as the dipole term is present.

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Section: Introductionmentioning

confidence: 99%

Schrödinger equation for non-pure dipole potential in 2D systems

Moumni

Falek

2016

Journal of Mathematical Physics

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“…Differential equations of the form similar to Equation (15) arise in many areas of both physics and quantum chemistry, ranging from the study of the harmonium to the confinement potentials [38][39][40][41][42][43][44][45][46]. Various exact and approximate methods are known for solving such an equation with central potentials [47][48][49][50][51][52][53][54][55].…”

Section: Four Methods Leading To Quantizationmentioning

confidence: 99%

“…It is obvious from these expressions that, while the requirement N (a, 0, c, d) = 0 would indeed give a genuine quantization condition, as it involves a single equation in all the parameters of the system, it is not at all useful in practice as it requires one to find the zeros of the infinite series (46) in order to be able to extract the quantization condition.…”

Section: Using the Biconfluent Heun Equation: The Asymptotic Approachmentioning

confidence: 99%

Landau Levels in a Gravitational Field: The Schwarzschild Spacetime Case

Landry

Hammad

2021

Universe

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We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of the particle with a gravitational field. Two independent approaches are used to solve the relevant Schrödinger equation within the Newtonian approximation. It is found that both approaches yield qualitatively similar results within their respective approximations. With the goal of clarifying some results found in the literature concerning the use of a third independent approach for extracting the quantization condition based on a similar differential equation, we show that such an approach cannot yield a general and yet consistent result. We point out to the more accurate, but impractical, way to use such an approach; a way which does in principle yield a consistent quantization condition. We discuss how our results could be used to contribute in a novel way to the existing methods for testing gravity at the tabletop experiments level as well as at the astrophysical observational level by deriving the corrections brought by Yukawa-like and power-law deviations from the inverse-square law. The full relativistic regime is also examined in detail.

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“…Since the advent of quantum mechanics, several methods have been developed in order to find the exact energy spectrum of bound states in stationary quantum systems. The knowledge of these spectrum is necessary for several applications in many fields of physics and theoretical chemistry [1][2][3][4]. Such encouraging results have arisen some studies on the potential within the frame work of common wave equations of both non-relativistic and relativistic wave equations i. e. including Schrödinger, Duffin-Kemmer-Petiau (DKP), Klein-Gordon or Dirac equations [5][6][7][8][9][10].…”

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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Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton–Jacobi formalism

Cited by 8 publications

References 29 publications

Schrödinger equation for non-pure dipole potential in 2D systems

Schrödinger equation for non-pure dipole potential in 2D systems

Landau Levels in a Gravitational Field: The Schwarzschild Spacetime Case

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

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