New Bound State Energies for Spherical Quantum Dots in Presence of a Confining Potential Model at Nano and Plank’s Scales

Maireche, Abdelmadjid

doi:10.17756/nwj.2016-016

Cited by 31 publications

(40 citation statements)

References 28 publications

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“…in ordinary three dimensional spaces [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]:…”

Section: Introductionmentioning

confidence: 99%

New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

Maireche

2017

ILCPA

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Keywords:The Vibrational-Rotational Structure of Supersingular plus Coulomb potential, noncommutative space and phase, star product and Boopp's shift method.Abstract. In this study, three-dimensional modified time-independent Schrödinger equation of modified vibrational-rotational structure of supersingular plus Coulomb (v.r.s.c) potential was solved using Boopp's shift method instead to apply star product, in the framework of both noncommutativity three dimensional real space and phase (NC: 3D-RSP). We have obtained the explicit energy eigenvalues for ground state and first excited state for interactions in one-electron atoms. Furthermore, the obtained corrections of energies are depended on infinitesimal parameterswhich are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers:and the angular momentum quantum number m . We have also shown that, the usual states in ordinary three dimensional spaces for ordinary vibrational-rotational structure of supersingular plus Coulomb potential are canceled and has been replaced by new degenerated   1 2 2  l sub-states in the extended new quantum symmetries of (NC: 3D-RSP).

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“…in ordinary three dimensional spaces [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]:…”

Section: Introductionmentioning

confidence: 99%

New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

Maireche

2017

ILCPA

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“…In this sub-section we apply the same strategy, which we have seen in our previously works [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] …”

Section: Two-dimensional Spin-orbital Hamiltonian Operators For Nmkpmentioning

confidence: 99%

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

Maireche

2017

ILCPA

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Abstract. In this work, an analytical expression for the nonrelativistic energy spectrum of some diatomic molecules was obtained through the Bopp's shift method in the noncommutative (NC) two-dimensional real space-phase symmetries (NC: 2D-RSP) with a new modified Kratzer-type potential (NMKP) in the framework of two infinitesimal parameters θ and θ due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation. The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of twodimensional system are investigated. We have shown that, the new energy of diatomic molecule is the sum of ordinary energy of modified Kratzer-type potential, in commutative space, and new additive terms due to the contribution of the additive part of the NMKP. We have shown also that, the group symmetry of (NC: 2D-RSP) reduce to new sub-group symmetry of NC two-dimensional real space (NC: 2D-RSP) under new modified Kratzer-type interactions.

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“…The radial function ( ) nl R r for IHQP satisfying the following differential equation [30], ( ) We have been given a brief description of the MSE in GGS (NC-3D: RSP) on based to our previously works [22][23][24][25][26][27]. To achieve this goal, we apply the important 4-steps on the ordinary SE: …”

Section: The Ihqp In Ordinary 3-dimensional Spacesmentioning

confidence: 99%

New Exact Non-relativistic Energy Eigen Values for Modified Inversely Quadratic Hellmann Plus Inversely Quadratic Potential

Maireche¹

2017

J Nanosci Curr Res

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In this current research, the solutions of modified Schrödinger equation (MSE) are presented for two companied potentials namely: modified inversely quadratic Hellmann potential and modified inversely quadratic potential (MIHQP), using generalization of Bopp's shift method (instead to solving MSE with star product) and standard perturbation theory in extended quantum mechanics (EQM), we obtained modified Hamiltonian operator and corresponding modified eigenvalues in both three dimensional noncommutative space and phase (NC-3D: RSP) symmetries. Citation: Maireche A (2017) New Exact Non-relativistic Energy Eigen Values for Modified Inversely Quadratic Hellmann Plus Inversely QuadraticPotential. J Nanosci Curr Res 2:115.

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New Bound State Energies for Spherical Quantum Dots in Presence of a Confining Potential Model at Nano and Plank’s Scales

Cited by 31 publications

References 28 publications

New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

New Exact Non-relativistic Energy Eigen Values for Modified Inversely Quadratic Hellmann Plus Inversely Quadratic Potential

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