SALIM Medjber

Bencharif Wissame

Dynamique quantique d'un oscillateur harmonique couplé dépendant du temps à 2D

TOUMI Soumia

La solution de l’équation de Schrödinger pour le potentiel de Morse généralisé utilisant la méthode de l’analyse fonctionnelle de Nikiforov–Uvarov (NUFA)

TOUMI Soumia

La solution de l’équation de Schrödinger pour le potentiel de Morse généralisé utilisant la méthode de l’analyse fonctionnelle de Nikiforov-Uvarov (NUFA)

Boudissa Oumbarka , Bendjoudi Atika

La solution de l’équation de Schrödinger dépendante du temps pour un oscillateur à 2D dans l’espace-phase non commutative

Bendaoud Elkhansa , Chami Karima

La solution de l'équation de Schrödinger dépendante du temps pour le potentiel de Morse

Seraiche Fatiha

La solution de l'équation de Schrödinger stationnaire et non stationnaire pour le potentiel hyperbolique

Saidi Assia

Solution de l'équation de Schrödinger dépendante du temps pour un potentiel non central avec de plus un potentiel coulombien et un potentiel quadratique inverse

Aouamer Souhila

Solution de l'équation de Schrödinger non stationnaire pour un potentiel singulier non central

Achouche Nacer

L'oscillateur harmonique couplé dépendant du temps

Belkaibech Oumelkheir

La solution de l'équation de Schrödinger pour le potentiel de Morse dépendant du temps

Baghdad Badra

La solution de l'équation de Schrödinger pour le potentiel de Woods-Saxon dépendant du temps

The time dependent Schrödinger equation for The Eckart potential is studied. This potential is not studied in the literatures. The Eckart potential is a superposition of the Coulomb potential and the Yukawa potential. The Eckart potential is a diatomic molecular potential model widely used in applied Physics and chemical Physics. To obtain the energies spectrum and the wave functions we use a new method called Nikiforov–Uvarov-Functional Analysis (NUFA) method and the method of variables separation. The (NUFA) method is composed of the concepts of the Nikiforov-Uvarov (NU) method, the parametric Nikiforov-Uvarov method and the functional analysis method. This method is a simple and elegant method for solving a second order differential equation of the hypergeometric type. This method is easy and simple just as the parametric NU method. Unlike the NU method which involved looking for the square of the polynomials and other conditions which makes it complicated, the (NUFA) method can easily be used to obtain the energy and the wave function once the wave equations have been properly transformed and the singularities identified. So its simplicity eliminates the rigorous mathematical manipulations, as encountered in other techniques. This method can be used to solve few body problems in nuclear physics, particle physics, as well as molecular and chemical physics. Keywords: The Nikiforov–Uvarov-Functional Analysis method, time dependent Schrödinger equation, Eckart potential

Citation

Salim MEDJBER , ,(2023-12-02), Approximation solutions of time dependent Schrodinger equation for Eckart potential using the Nikiforov-Uvarov-Functional Analysis method,The 1st national conference on physics and its applications, NCPA2023,Higher normal school of Bousaada

The non-commutative geometry is a geometry where the coordinates of space-phase do not commute; it was designed both to meet needs in mathematics and to allow treating some theoretical physics problems . The noncommutativity was introduced firstly by Heisenberg W. in 1930 and then developed and formulated by Syndre H. in 1947 because of the need to regularize the divergence of the quantum field theory . Recently, physicists have developed previously works by applying the noncommutativity properties on space and phase . The noncommutativity get more investigation in the microscopic scales and achieve more scientific knowledge of elementary particles in the field of nanotechnology, and it is shown a direct relationship between string theory and noncommutative geometry and to obtaining profound and new applications for different areas of matter sciences in the microscopic and nano scales within the framework of quantum mechanics and quantum field theory . The aim of this work is to study the hydrogenoid atoms in a noncommutative space, this noncommutativity was considered as a time-independent perturbation in the expression of the Coulomb potential. I then made some resulting corrections in the expression of Bohr energies and fine structure energies. I came to a conclusion that the noncommutativity lifted the degeneracy of the energies, and induced a shift in the spectrum of the energies. Keywords: Schrödinger equation, the hydrogenoid atom, Coulomb potential, noncommutative space-phase, the Weyl Moyal star product, the Bopp’s shift method.

Citation

Salim MEDJBER , ,(2023-05-10), Quantum study for hydrogenoid atoms in non-commutative space,Computational and applied physics symposium CAPS2023,Université de Khemis Miliana

The time dependent Schrödinger equation for The Hellmann potential is studied. This potential is not studied in the literatures. The Hellmann potential is a superposition of the Coulomb potential and the Yukawa potential. The knowledge of the solution of the Schrodinger equation gave all the possible information, as regards the physical properties of any system considered. These include the energy, momentum and coordinate of the particle in the system, frequency and wavelength that describe the quantum mechanical system, probability amplitude and phase of the wave function, and others. To obtain the energies spectrum and the wave functions we use a new method for solving a second order differential equation of the hypergeometric type called Nikiforov–Uvarov-Functional Analysis (NUFA) method and the method of variables separation . The (NUFA) method is composed of the concepts of the Nikiforov-Uvarov (NU) method, the parametric Nikiforov-Uvarov method and the functional analysis method. This method is a simple and elegant method for solving a second order differential equation of the hypergeometric type. This method is easy and simple just as the parametric NU method. Unlike the NU method which involved looking for the square of the polynomials and other conditions which makes it complicated, the NUFA can easily be used to obtain the energy and the wave function once the wave equations have been properly transformed and the singularities identified. So its simplicity eliminates the rigorous mathematical manipulations, as encountered in other techniques. This method can be used to solve few body problems in nuclear physics, particle physics, as well as molecular and chemical physics. Keywords :The Nikiforov–Uvarov-Functional Analysis method, time dependent Schrödinger equation, Hellmann potential, wave function, method of variables separation

Citation

Salim MEDJBER , ADMIN Admin , Menouar salah, ,(2023-04-18), Approximation solutions of time dependent Schrodinger equation for Hellmann potential using the Nikiforov-Uvarov-Functional Analysis method,1stInternational Conference on Scientific and Innovative Studies,Konya, Turky

The time dependent Schrödinger equation for the deformed Woods-Saxon potential is studied. This potential is not studied in the literatures. The deformed Woods-Saxon potential was used for description of interaction of a nucleon with a heavy nuclear The knowledge of the solution of the Schrodinger equation gave all the possible information, as regards the physical properties of any system considered. These include the energy, momentum and coordinate of the particle in the system, frequency and wavelength that describe the quantum mechanical system, probability amplitude and phase of the wave function, and others. To obtain the energies spectrum and the wave functions we use a new method for solving a second order differential equation of the hypergeometric type called Nikiforov–Uvarov-Functional Analysis (NUFA) method and the method of variables separation. The (NUFA) method is composed of the concepts of the Nikiforov-Uvarov (NU) method, the parametric Nikiforov-Uvarov method and the functional analysis method. Unlike the NU method which involved looking for the square of the polynomials and other conditions which makes it complicated, the NUFA can easily be used to obtain the energy and the wave function once the wave equations have been properly transformed and the singularities identified. So its simplicity eliminates the rigorous mathematical manipulations, as encountered in other techniques. The eigensolutions obtained using NUFA method are in agreement with the ones obtained in literatures for the stationary potential models considered. Keywords: The Nikiforov–Uvarov-Functional Analysis method, time dependent Schrödinger equation, deformed Woods-Saxon potential, wave function, method of variables separation.

Citation

Salim MEDJBER , ADMIN Admin , Menouar Salah, ,(2023-03-10), Quantum dynamics of time dependent deformed Woods-Saxon potential using the Nikiforov-Uvarov-Functional Analysis method,2nd International Conference on Scientific and Academic Research,Konya, Turkey

The one-dimensional Klein-Gordon equation is solved for the equal scalar and vector generalized Hulthén potential. The Nikiforov–Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding normalized eigenfunctions. Keywords: The Klein-Gordon equation, the generalized Hulthén potential, The Nikiforov–Uvarov method.

Citation

Salim MEDJBER , ,(2023), Exact solution of one dimensional Klein-Gordon equation for generalized Hulthen potential by the Nikiforov-Uvarov method,3rdInternational Conference on Engineering and Applied Natural Sciences ICEANS2022,Konya, Turky

Exact quantum solutions of the Schrödinger equation for the time-dependent Coulomb potential plus an inverse-square-root potential isstudied by using the invariant operator and extended Nikiforov-Uvarov method. Eigenstate solutions and its corresponding eigenvaluesare obtained in a systematic way without using the method of invariant and unitary transformation. The complete solutions for considered potential are given in terms of biconfluentHeun polynomials.The results obtained are compared with the stationary case. Keywords:Schrödinger equation,Unitary transformation, Coulomb potential, Inverse-square-root potential, Invariant method.

Citation

Salim MEDJBER , Salah Menouar, ,(2023), Exact quantum study of time-dependent Coulomb potential plus an inverse-square-root potential,2nd International Conference on Innovative Academic Studies,Konya, Turky

Exact solutions of the Schrödinger equation for the time-dependent inverse-square-root potential is presented by using the extended Nikiforov-Uvarov method. Eigenstate solutions are obtained in a systematic way without using the method of invariant and unitary transformation. The complete solutions for considered potential is given in terms of biconfluentHeun polynomials. Keywords: Schrödinger equation, Inverse-square-root potential, Invariant method.

Citation

Salim MEDJBER , Salah Menouar, ,(2023), Quantum study of time-dependent inverse-square-root potential,3rd International Conference on Engineering and Applied Natural Sciences,Konya, Turky

The stationary and non stationary Schrödinger equation is solved for the one dimensional hyperbolic potential. Solution of stationary potential is obtained reducing the Schrödinger equation into a second order differential by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get the energy eigenvalus and the corresponding wave functions. For the non stationary potential, we are using the separation variable method to obtain the spectrum energy and the wave functions corresponding. Keywords: Schrödinger equation, Nikiforov-Uvarov method, hyperbolic potential, separation variable method wave function.

Citation

Salim MEDJBER , ,(2022), The exact solution of the stationary and non stationary Schrödinger equation for hyperbolic potential,1st International Conference on Scientific and Academic Research,Konya, Turky

The approximate analytical solutions of the radial Klein –Gordon equation have been obtained with a equally scalar and vector of newly proposed potential called Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential and generalized Morse or Deng-Fan potential. The Hellmann-generalized Morse potential actually comprises of three different potentials which includes Yukawa potential, Coulomb potential and Deng-Fan potential. The aim of combining these potentials is to have a wide application. The energy eigenvalues and the corresponding wave functions are calculated in a closed and compact form using the parametric Nikiforov-Uvarov method. The Nikiforov–Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding normalized eigenfunctions. Keywords: Klein–Gordon equation, Hellmann-generalized Morse potential, Yukawa potential, Coulomb potential, Nikiforov–Uvarov method.

Citation

Salim MEDJBER , ,(2022), Arbitrary l state solutions of the Klein Gordon equation with Hellmann generalized Morse potential,1st International Conference on Engineering, Natural and Social Sciences ICENSOS 2022 o,Konya, Turky

The Gaussian wave packet (GWP) has been extensively by physicist and chemist in studying the time evolution of various dynamical systems. We obtained the exact solution of the Schrödinger equation for no stationery general quadratic harmonic oscillator which is the semi classical Gaussian wave packet centred around the classical guiding trajectory .Gaussian wave packets are appearing in quantum mechanics and are fundamental states of many physical systems that exhibit various nonclassical properties. Keywords : Gaussian wave packet; Schrödinger equation; quadratic harmonic oscillator.

Citation

Salim MEDJBER , Hacene Bekkar, Salah Menouar, ,(2022), Gaussian wave packet for no stationery generalized harmonic oscillator,1st International Conference on Engineering, Natural and Social Sciences ICENSOS 2022,Konya, Turky

In This work we studied the exact solutions of the one dimensional Schrödinger equation with a time-dependent Coulomb potential (-Z(t)/|x|) based on the formalism of quantum invariant theory ( Lewis and Riesenfeld theorem). Using the technique of unitary transformation with a relevant choice of an invariant operator, we have obtained the eigenfunctions and the corresponding energy eigenvalues of the system. Due to the singularity at the origin, solutions are obtained separately for the region x>0 and x<0, and then matched appropriately at x=0. The solution of the problem here is expressed in terms of associated Laguerre functions (regular solution), z(t)=z₀ our wavefunction is fully equivalent to the 3D Hydrogen problem in the case of the zero angular momentum which nullifies the centrifugal potential terms. The results we examined for this potential are comparable to those obtained in the stationary case. Keywords : Coulomb potential; Schrödinger equation; Dynamical invariant; wavefunctions.

Citation

Salim MEDJBER , Salah Menouar, ,(2022), Quantum study of the one dimensional Coulomb potential with a time dependent electrical charge,1st International Conference on Engineering, Natural and Social Sciences ICENSOS 2022,Konya, Turky

We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators.

Citation

Salim MEDJBER , Salah Menouar, Jeong Ryeol Choi, , (2021), Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators, Entropy, Vol:23, Issue:7, pages:14, MDPI

We have obtained the exact solution of the time-independent and time-dependent Schrodinger equation governing the two dimensional harmonic oscillator in non-commutative space-phase. We write the Hamiltonian of the system in terms of creation and annihilation operators(a_i,a_i^+), and then we solve the time-independent and time-dependent Schrodinger equation under the condition M(t)Ω(t)=const. For the stationary Schrodinger equation we use the algebraic method. For non stationary Schrodinger equation we use the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation.

Citation

Salim MEDJBER , ,(2021), The exact solution of the stationary and non stationary Schrodinger equation for bidimensional harmonic oscillators in non-commutative space-phase,1er congres national de physique théorique,Tlemcen

Ce polycopié est avant tout un ensemble d’exercices et de problèmes résolus avec des rappels de cours de la mécanique du point matériel conforme au programme de la première année tronc commun (LMD). C’est un outil de travail qui s’adresse aux étudiants de la première année des filières SM (sciences de la matière) semestre1. Cet ouvrage est conçu pour apporter aux étudiants une aide dans leur cursus et leur permet de progresser. Il existe pour accompagner l’étudiant dans son travail personnel. Nous espérons que ce rappel de cours et d’exercices résolus, aidera nos étudiants à comprendre la mécanique du point matériel. Ce polycopié contient les chapitres suivants: - chapitre I : Rappel mathématique - chapitre II : Cinématique du point matériel - chapitre III : Mouvement relatif - chapitre IV : Dynamique du point matériel. - chapitre V : Travail et énergie.

Citation

SalimMEDJBER , ,(2021); Mécanique du point matériel,M'sila,

The non stationary Schrodinger equation is exactly solved for the one dimensional inverse square root potential: V(x,t)=V_0 (t)/√x. To solve this equation we use the invariant method. Each of the two fundamental solutions that compose the general solution of the problem is giving by a combination with the non-constant coefficients of two confluent hypergemetric functions of a shift argument. Alternatively, the solution is written through the first derivative of a tri-confluent Heun function. The spectrum energy is giving by: E_n (t)=E_1 (t) n^(-2/3) .

Citation

Salim MEDJBER , Hacene Bekkar, ,(2020), Exact solution of the non stationary Schrodinger equation for one dimensional the inverse square root potential,3rd international conference on physic chemistry and functional materials ( PCFM 2020),Malatya, Turkey

We present the exact solution of Schrödinger equation for the one dimensional non stationary Morse potential. To solve this equation we use the separation of variables method. We are reducing this equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov (N-U) method is used in the calculations to get energy eigenvalues and corresponding wave functions.

Citation

Salim MEDJBER , Hacene Bekkar, ,(2020), Exact solution of the Schrödinger equation for one dimensional non stationary Morse potential,3rd international conference on physic chemistry and functional materials ( PCFM 2020),Malatya, Turkey

We have introducing the fundamental tools of the formalism of nonrelativistic quantum mechanics based on a generalized uncertainly principle, implying the existence of a minimal length. We consider a simple system namely the one dimensional linear potential to illustrate how the stationary and non stationary Schrödinger equation in the presence of the minimal length can be solved exactly. For a non stationary Schrödinger equation the wave functions obtained is written as a Gaussian wave packet. Keywords: Schrödinger equation, minimal length, deformed quantum mechanics, linear potential, Gaussian wave packet.

Citation

Salim MEDJBER , ,(2018), Gaussian wave packet solution of the stationary and non stationary Schrodinger equation for linear otential in presence of minimum length,1ère Rencontre de Physique Théorique,Jijel, Algeria

Ce polycopié est destiné aux étudiants du semestre 3 des sciences techniques du système LMD pour la spécialité de la physique théorique. Il contient un cours abrégé sur la physique statistique classique et quantique. Ce polycopié contient les chapitres suivants: - chapitre I : Ensemble Canonique et Ensemble grand Canonique - chapitre II : Formulation de la statistique quantique - chapitre III : Système de bosons - chapitre IV : Système de fermions - chapitre V : Etude des systèmes quantiques hors équilibre

Citation

SalimMEDJBER , ,(2018); Physique statistique classique et quantique,M'sila,

The research for quantum future of molecular Coulomb interactions subjected to a time-dependent non-central potential has many applications. The wave function of this system can be ontained by using an invarian operator, which is necessary for investigating a time-dependent Hamiltonian system. regarding time dependence of the system, one can confirm that the formula of this operator is in general somewhat complicated. Hence, in order to solve its eigenvalue equation, special mathematical techniques beyond separation of variables method, such as the unitary transfomation method, the Nikiforov-Uvarov method, and the asymtotic iteration method, should be employed . The double ring-shaped generalized non central potetial of which evolution explicity depends on time is introduced as a particular case. The complete quatum solutions of the system can be identifed from the eigenstatess of the invarian operator. Thes solutions are useful for analysing dynamical properties of the system

Citation

Salim MEDJBER , Jeong Ryeol Choin, Salah Menouar, Hacene Bekkar, , (2017), Quantum features of molecular interactions associated with time dependent non-central potentials, Journal of Physics Communications, Vol:3, Issue:7, pages:17, salim medjber

The relashionship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schrodinger equation for the Caldirola-Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied using the invariant theory of Lewis and Riesenfeld . In particular, we analyse time behaviours of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problem. Keywords: Ehrenfest theorem, invariant theory, time dependent Hamiltonian system

Citation

Salim MEDJBER , , (2016), the validity of the Ehrenfest theorem beyond simple static systems: Caldirola-Kanai oscillator driven by a time-dependent force, Chinese physics B, Vol:25, Issue:8, pages:6, Medjber salim

The Schrodinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential system are investigated. Because of the time-dependence of parameters, we cannot solve the Schrodinger equation relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrodinger equation for the system. In particular, and the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrodinger solutions (wave functions) of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertaintly relations for for position and momentum are derived by taking advantage of the wave functions. Keywords: invariant theory, Nikiforov-Uvarov method , unitary transformation method , time-dependent harmonic plus an inverse harmonic potential

Citation

Salim MEDJBER , , (2016), of 3D nonstationary harmonic plus inverse harmonic potential system, Advances in Mathematical Physics, Vol:24, Issue:4, pages:6, Medjber Salim

The one dimensional Schrodinger equation associated with a time-dependent Morse potential is studied. We use the invariant operator method (Lewis and Riesenfeld) to obtain exact solution of the Schrodinger equation in terms of solution of second order ordinary differential equation describes the amplitude of the Morse potential. Keywords: Schrödinger equation , invariant method, Morse potential, time dependent systems

Citation

Salim MEDJBER , , (2014), Wave functions for time dependent Morse potential, Journal of Mathematical and System Science, Vol:20, Issue:4, pages:3, Medjber Salim

The one dimensional Schrodinger equation associated with a time-dependent Woods-Saxon (W-S) potential is studied. We use the invariant operator method (Lewis and Riesenfeld) to obtain exact solution of the Schrodinger equation in terms of solution of second order ordinary differential equation describes the amplitude of the (W-S) potential. Keywords: Time dependent Schrödinger equation, invariant method, time-dependent

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Salim MEDJBER , ,(2014), Exact wave functions for time dependent Woods-Saxon potential,The 4th International Advanced in Applied Physics and Material Science Congress &Exhibition (APMAS 2014),Fethiye, Mugla-Turky

Newly different methods have been adopted for the solution of the Schrodinger equation (SE) with various potentials such methods include numerical and analytical techniques, supersymmetry, Pekeris approximation and the Nikiforov-Uvarov method. An exact solution of the SE is of high importance in non-relativistic quantum mechanics. However, there are very little potential for which the radial SE can be solved exactly for all n and l-values. Keywords: Schrödinger equation, Nikiforov-Uvarov method, Hulthén potential

Citation

Salim MEDJBER , ,(2013), Approximate solution of Schrodinger equation for Hulthén potential plus Colombian term,the 9th International Conference in Subatomic Physics and Applications,constantine, Algeria