A semi-inverse variational method for generating the bound state energy eigenvalues in a quantum system: The Schrödinger equation

Zerarka, A.; Libarir, K.

doi:10.1016/j.cnsns.2008.11.008

Cited by 19 publications

(3 citation statements)

References 15 publications

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“…We put the equation ( 7) under the consistency condition (8). It is simple to confirm that this criterion is not met.…”

Section: ′′mentioning

confidence: 99%

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Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic- and perturbed Coulomb potentials

Reggab,

Gueddim,

Naas

2023

SEES

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The events observable at the atomic scale cannot be adequately explained by classical physics, hence a new conceptual framework for physics must be developed. "Quantum mechanics" is the name given to this new theory of the physical cosmos. The basic formula of relativistic quantum mechanics is the problem of Klein-Gordon. In relativistic quantum physics, the wave function is crucial since it contains all the data describing a quantum system, in relativity quantum physics, they are crucial. How to solve Klein Gordon's equation has been the topic of intense debate in recent years. To determine the system's spectrum using numerous potentials and methodologies. To obtain the Klein-Gordon issues solution Through determining the harmonic and perturbed Coulomb potentials' energies, The recent study employed an entirely distinct methodology. using the Semi-Inverse Variational Technique to aid in the process, we were able to identify the eigen energies for Harmonic- and Perturbed Coulomb Potentials for a variety of quantum numbers. A further benefit of the technique was that it enabled us to obtain the wave eigenfunctions for various potentials, demonstrating the viability of this approach. We are excited to deal with additional challenges in our upcoming works, the first being the use of nonlinear potentials to solve the Dirac equation due to the effectiveness of this approach.

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“…We put the equation ( 7) under the consistency condition (8). It is simple to confirm that this criterion is not met.…”

Section: ′′mentioning

confidence: 99%

“…In this study, we resolved the Klein-Gordan equation using the semi-inverse variational approach. Abdelouahab Zerarka [8][9][10], Zhou Xin-Wrei [11][12], and Liu Hong-Mei [13][14] have all employed this semi-inverse variational technique in the past in various situations. In Refs.…”

Section: Introductionmentioning

confidence: 99%

Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic- and perturbed Coulomb potentials

Reggab,

Gueddim,

Naas

2023

SEES

View full text Add to dashboard Cite

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“…Specifically, Various approaches have been employed to examine the resolutions of the Schrödinger formula with different types of potentials. [10][11][12][13][14][15][16] The objective of this study is to incorporate the NU into the existing framework [17],…”

Section: Introductionmentioning

confidence: 99%

Energy spectrum of selected diatomic molecules (H2, CO, I2, NO) by the resolution of Schrodinger equation for combined potentials via NUFA method

Reggab

2024

J Mol Model

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The equation proposed by Schrödinger is widely recognized as the foundational formula in quantum science, comparable to the law of gravity in the study of classical physics.Describing phenomena in various fields, such as quantum optics and atomic physics, exhibits significant diversity. For specific diatomic molecule potentials, analytical responses to the Schrodinger formula can be found. These responses cover all possible values of angular momentum. The NU functional analysis and the Greene-Aldrich hypothesis are employed in our study for the purpose of obtaining an approximate solution for the Schrödinger issue including a screened modified Kratzer potential combined with an inverse quadratic Yukawa potential, a systematic approach needs to be employed. In this study, we calculate the energy eigenvalues associated with bound states in various quantum states, the present study focuses on a distinct group of diatoms molecules. The analytical data that were acquired are utilized in the analysis of various diatomic compounds H2, CO, I2, and NO. A comparative analysis compares the results of this study to those found in other studies that used different methods to figure out how accurate the current method is.

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Bounded solution structure of Schrödinger equation in the presence of the minimal length and its effect: Bound states in the continuum are universal

Zhang

Yang

Wei

et al. 2021

Communications in Nonlinear Science and Numerical Simulation

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A semi-inverse variational method for generating the bound state energy eigenvalues in a quantum system: The Schrödinger equation

Cited by 19 publications

References 15 publications

Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic- and perturbed Coulomb potentials

Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic- and perturbed Coulomb potentials

Energy spectrum of selected diatomic molecules (H2, CO, I2, NO) by the resolution of Schrodinger equation for combined potentials via NUFA method

Bounded solution structure of Schrödinger equation in the presence of the minimal length and its effect: Bound states in the continuum are universal

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