Exact solution of N-dimensional radial Schrödinger equation for the fourth-order inverse-power potential

Khan, Gulzar

doi:10.1140/epjd/e2009-00096-6

Cited by 19 publications

(17 citation statements)

References 25 publications

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“…With the help of equations (32) and (33a)-(33e), the expansion coefficients a n in equation (35) satisfy the following recursion relation [72] a n+1 = 4λ 2 −9−4(n+λ+2) 2(n+λ+2) 2 a n−1 .…”

Section: 、Generalized Dirac Oscillator With a Topological Defectmentioning

confidence: 99%

Generalized Dirac Oscillator in Cosmic String Space-Time

Deng

Long

et al. 2018

Advances in High Energy Physics

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In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum p μ with its alternative p μ + mωβf μ (x μ ). In particular, the quantum dynamics is considered for the function f μ (x μ ) to be taken as cornell potential, exponential-type potentialand singular potential. For cornell potential and exponential-type potential, the corresponding radial equations can be mapped into the confluent hypergeometric equation and hypergeometric equation separately. The corresponding eigenfunctions can be represented as confluent hypergeometric function and hypergeometric function.The equations satisfed by the exact energy spectrum have been found. For singular potential, the wave function and energy eigenvalue are given exactly by power series method.

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Section: 、Generalized Dirac Oscillator With a Topological Defectmentioning

confidence: 99%

Generalized Dirac Oscillator in Cosmic String Space-Time

Deng

Long

et al. 2018

Advances in High Energy Physics

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“…The surface element in D spatial dimension is DC D r D−1 dr, where the explicit expression of the terms C D has been stated in section 2.1. As the wave function in this case contains Airy's infinite polynomial series, we calculate < H > through numerical integration using the following integrals: (27) In this case, with Airy's function involved in the wave function, simpler equations like (13)(14)(15)(16)(17)(18)(19)(20)(21)(22) in the large D limit are not possible as we follow numerical integration to evaluate terms < H 1 >, < H 2 >, < H 3 >.…”

Section: Mass With Linear Term As Parentmentioning

confidence: 99%

Effective string theory inspired potential and meson masses in higher dimension

Roy¹,

Choudhury

2016

Can. J. Phys.

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Nambu-Goto action in classical bosonic string model for hadrons predicts quark-antiquark potential to be[1] V (r) = − γ r + σr + µ0. In this report we present studies of masses of heavy flavour mesons in higher dimension with our recently developed wave functions obtained following string inspired potential. We report the dimensional dependence of the masses of mesons. Our results suggest that as the meson mass increases with the number of extra spatial dimension, it will attain the Planck scale (∼ 10 19 GeV ) asymptotically at an astronomically large spatial dimension (we call it Planck dimension) D P lanck ∼ 10 11 , which sets the limit of applicability of Schrodinger equation in large dimension.

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“…In the recent B Damian Mikulski dmkwant@amu.edu.pl 1 years authors have analytically derived exact solutions for diverse potentials, i.a. the fourth-order inverse power potential [1][2][3]:…”

Section: Introductionmentioning

confidence: 99%

Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

Mikulski¹,

Konarski

Eder³

et al. 2015

J Math Chem

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The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules.

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Exact solution of N-dimensional radial Schrödinger equation for the fourth-order inverse-power potential

Cited by 19 publications

References 25 publications

Generalized Dirac Oscillator in Cosmic String Space-Time

Generalized Dirac Oscillator in Cosmic String Space-Time

Effective string theory inspired potential and meson masses in higher dimension

Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

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