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

2017 ◽  
Vol 73 ◽  
pp. 31-45 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Bound States ◽  
Star Product ◽  
Three Dimensional ◽  
Real Space ◽  
Rotational Structure ◽  
Angular Momentum Quantum Number ◽  
Quantum Symmetries

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 parameters (Θ,χ) and (θ,σ) which are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers: j=l±1/2,s=±1/2,l 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spaces for ordinary vibrational-rotational structure of supersingular plus Coulomb potential are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended new quantum symmetries of (NC: 3D-RSP).

scholarly journals A New Study to the Schrödinger Equation for Modified Potential V(r)=ar2+br-4+cr-6 in Nonrelativistic Three Dimensional Real Spaces and Phases

2015 ◽  
Vol 61 ◽  
pp. 38-48 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Three Dimensional ◽  
Noncommutative Space ◽  
Shift Method ◽  
First Order ◽  
Standard Perturbation Theory

In present work, by applying Boopp’s shift method and standard perturbation theory we have generated exact nonrelativistic bound states solution for a modified potential (see formula in paper) in both three dimensional noncommutative space and phase (NC: 3D-RSP) at first order of two two infinitesimal parameters antisymmetric (see formula in paper), we have also derived the corresponding noncommutative Hamiltonian.

scholarly journals EXACT SOLUTIONS OF THE MODIFIED KRATZER POTENTIAL PLUS RING-SHAPED POTENTIAL IN THE D-DIMENSIONAL SCHRÖDINGER EQUATION BY THE NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 19 (02) ◽  
pp. 221-235 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Laguerre Polynomials ◽  
Three Dimensional ◽  
Wave Functions ◽  
Modified Kratzer Potential ◽  
Energy Bound ◽  
Uvarov Method ◽  
Exact Energy

We present analytically the exact energy bound-states solutions of the Schrödinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov–Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.

scholarly journals The noncommutative Coulomb potential

2021 ◽  
pp. 2150094
Author(s):  
B. C. Wang ◽  
E. C. Brenag ◽  
R. G. G. Amorim ◽  
V. C. Rispoli ◽  
S. C. Ulhoa
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Potential Problem ◽  
Energy Levels ◽  
Three Dimensional

In this work, we analyze the noncommutative three-dimensional Coulomb potential problem. For this purpose, we used the Kustaanheimo–Stiefel mapping to write the Schrödinger equation for Coulomb potential in a solvable way. Then, the noncommutative hydrogen-like atoms were treated, and their energy levels were found. In addition, we estimate a bound for the noncommutativity parameter.

scholarly journals A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

2016 ◽  
Vol 10 ◽  
pp. 8-22
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Star Product ◽  
Three Dimensional ◽  
Spin Symmetry ◽  
Hamiltonian Operator ◽  
Bound State ◽  
Exact Bound ◽  
Quantum Numbers ◽  
Quantum Symmetries

New exact bound state solutions of the deformed radial upper and lower components of Dirac equation and corresponding Hermitian anisotropic Hamiltonian operator are studied for the modified Kratzer-Fues potential (m.k.f.) potential by using Bopp’s shift method instead to solving deformed Dirac equation with star product. The corrections of energy eigenvalues are obtained by applying standard perturbation theory for interactions in one-electron atoms. Moreover, the obtained corrections of energies are depended on two infinitesimal parameters (θ,χ), which induced by position-position noncommutativity, in addition to the discreet nonrelativistic atomic quantum numbers: (j=l±1/1,s=±1/2,landm) and we have also shown that, the usual relativistic states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended quantum symmetries (NC: 3D-RS).

scholarly journals EXACT QUANTIZATION RULES FOR BOUND STATES OF THE SCHRÖDINGER EQUATION

2005 ◽  
Vol 14 (04) ◽  
pp. 599-610 ◽  
Author(s):  
ZHONG-QI MA ◽  
BO-WEI XU
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Three Dimensional ◽  
Spherically Symmetric ◽  
Quantization Rule ◽  
One Dimensional ◽  
Exact Quantization Rule ◽  
The One ◽  
Quantization Rules

An exact quantization rule for the bound states of the one-dimensional Schrödinger equation is presented and is generalized to the three-dimensional Schrödinger equation with a spherically symmetric potential.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

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