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Volume 58
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New Exact Solution of the Bound States for the Potential Family V(r)=A/r<sup>2</sup>-B/r+Cr<sup>k</sup> (k=0,-1,-2) in both Noncommutative Three Dimensional Spaces and Phases: Non Relativistic Quantum Mechanics
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New Exact Solution of the Bound States for the Potential Family V(r)=A/r2-B/r+Crk (k=0,-1,-2) in both Noncommutative Three Dimensional Spaces and Phases: Non Relativistic Quantum Mechanics

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Abstract:

In present work we obtain the modified bound-states solutions for central family V(r)=A/r2-B/r+Crk (k=0,-1,-2) in both noncommutative three dimensional spaces and phases. It has been observed that the energy spectra in ordinary quantum mechanics was changed, and replaced degenerate new states, depending on two infinitesimals parameters Θ and θ corresponding the noncommutativity of space and phase, in addition to the discrete atomic quantum numbers: j, l, sz=+-1/2 and corresponding to the two spins states of electron by (up and down) and non polarized electron. The deformed anisotropic Hamiltonian formed by three operators: the first describes usual the usual family potential, the second describe spin-orbit interaction while the last one describes the modified Zeeman effect (containing ordinary Zeeman effect).

Info:

Periodical:
International Letters of Chemistry, Physics and Astronomy (Volume 58)
Pages:
164-176
DOI:
https://doi.org/10.18052/www.scipress.com/ILCPA.58.164
Citation:
A. Maireche, "New Exact Solution of the Bound States for the Potential Family V(r)=A/r2-B/r+Crk (k=0,-1,-2) in both Noncommutative Three Dimensional Spaces and Phases: Non Relativistic Quantum Mechanics", International Letters of Chemistry, Physics and Astronomy, Vol. 58, pp. 164-176, 2015
Online since:
September 2015
Authors:
Abdelmadjid Maireche
Keywords:
Boopp's Shift Method, Family Potential, Noncommutative Phase, Noncommutative Space, Star Product, V(r)=A/r2-B/r+Crk (k=0,-1,-2)
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Distribution:
Open Access

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

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Cited By:

[1] 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

[2] 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

[3] 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