A New Approach to the Non Relativistic Schrödinger Equation for an Energy-Depended Potential V(r,En,l)=V0(1+ηEn,l)r2 in both Noncommutative Three Dimensional Spaces and Phases

Maireche, Abdelmadjid

doi:10.18052/www.scipress.com/ILCPA.60.11

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A New Approach to the Non Relativistic Schrödinger Equation for an Energy-Depended Potential V(r,E_n,l)=V₀(1+ηE_n,l)r² in both Noncommutative Three Dimensional Spaces and Phases

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Abstract:

In present work we study the 3-dimensional non relativistic and noncommutative space-phase Schrödinger equation for modified potential (see formula in paper) depends on energy and quadratic on the relative distance, we have obtained the exact modified bound-states solutions. It has been observed that, the energy spectra in ordinary quantum mechanics was changed, and replaced by degenerate new states, depending on new discreet quantum numbers:n, l, j and s=±1/2 . We show the noncommutative new anisotropic Hamiltonian containing two new important terms, the first new term describe the spin-orbit interaction while the second describes the modified Zeeman effect.

Info:

Periodical:

International Letters of Chemistry, Physics and Astronomy (Volume 60)

Pages:

11-19

DOI:

https://doi.org/10.18052/www.scipress.com/ILCPA.60.11

Citation:

A. Maireche, "A New Approach to the Non Relativistic Schrödinger Equation for an Energy-Depended Potential V(r,E_n,l)=V₀(1+ηE_n,l)r² in both Noncommutative Three Dimensional Spaces and Phases", International Letters of Chemistry, Physics and Astronomy, Vol. 60, pp. 11-19, 2015

Online since:

September 2015

Authors:

Abdelmadjid Maireche

Keywords:

Boopp’s Shift Method, Energy-Depended Potential, Noncommutative Phase, Noncommutative Space, Schrödinger Equation, Star Product

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Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

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Cited By:

[1] A. Maireche, "A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry", International Frontier Science Letters, Vol. 10, p. 8, 2016

DOI: https://doi.org/10.18052/www.scipress.com/IFSL.10.8

[2] A. Maireche, "A New Nonrelativistic Investigation for Interactions in One-Electron Atoms With Modified Inverse-Square Potential: Noncommutative Two and Three Dimensional Space Phase Solutions at Planck’s and Nano-Scales", Journal of Nanomedicine Research, Vol. 4, 2016

DOI: https://doi.org/10.15406/jnmr.2016.04.00090

[3] A. Maireche, "Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Anharmonic Oscillator", Journal of Nanomedicine Research, Vol. 4, 2016

DOI: https://doi.org/10.15406/jnmr.2016.04.00097

[4] O. Hegacy, "Model for End-Stage Liver Disease (Meld) Score, As a Prognostic Factor for Cirrhotic Patients, Undergoing Hepatectomy for Hepatocellular Carcinoma", Gastroenterology & Hepatology : Open Access, Vol. 2, 2015

DOI: https://doi.org/10.15406/ghoa.2015.02.00044

[5] A. Maireche, "A New Nonrelativistic Investigation for the Lowest Excitations States of Interactions in One-Electron Atoms, Muonic, Hadronic and Rydberg Atoms with Modified Inverse Power Potential", International Frontier Science Letters, Vol. 9, p. 33, 2016

DOI: https://doi.org/10.18052/www.scipress.com/IFSL.9.33

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