An-Najah Blogs :: Professor Sami M. AL-Jaber - Physics Department http://blogs.najah.edu/author/al-jaber An-Najah Blogs :: Professor Sami M. AL-Jaber - Physics Department en-us Fri, 28 Feb 2020 17:23:36 IST Fri, 28 Feb 2020 17:23:36 IST webmaster@najah.edu webmaster@najah.edu Some remarks on approximation methods for quantum systems in higher space dimensionshttp://blogs.najah.edu/staff/al-jaber/article/Some-remarks-on-approximation-methods-for-quantum-systems-in-higher-space-dimensionsPublished ArticlesAbstract We consider the effect of space dimension N on the results predicted by two approximation techniques applied on physical quantum systems In the first we apply degenerate perturbation theory to perturbed N-dimensional infinite cubical well It is found that the energy difference for splitting decreases as N increases and it vanishes in the infinite dimensional space In the second we apply the sudden approximation to the electronic structure change implied by beta-decay of the tritium nucleus It is found that as N increases the ionization probability increasesVariational method for ground-state energy of helium atom in N dimensionshttp://blogs.najah.edu/staff/al-jaber/article/Variational-method-for-ground-state-energy-of-helium-atom-in-N-dimensionsPublished ArticlesSami M AL-JaberDepartment of Physics An-Najah National University - PO Box 7 Nablus Palestine Abstract: The ground-state energy of the N-dimensional helium atom is presentedby applying the variational principle The calculations are made for theunscreened and screened cases It is shown that in both cases the magnitude ofthe ground-state energy decreases less negative as the spatial dimension N increasesFor the unscreened case the relative contribution of the electron-electroninteraction term to the ground-state energy is calculated for different dimensionsand it is found that this ratio approaches one half as N For the screenedcase the effective nuclear charge is computed for different dimensions and its limitingvalue is found to be 32 in the infinite-dimensional space In addition therelative contribution of screening to ground-state energy is calculated in differentdimensions and it is shown that it reaches 18 as N Furthermore the asymptoticbehavior of ground-state energy contribution of electron-electron interactionand contribution of screening effect are presentedMultidimensional electrostatic energy and classical renormalizationhttp://blogs.najah.edu/staff/al-jaber/article/Multidimensional-electrostatic-energy-and-classical-renormalizationPublished ArticlesRecent interest in problems in higher space dimensionsis becoming increasingly importantand attracted the attention of many investigatorsin variety of fields in physics In this paperthe electrostatic energy of two geometries acharged spherical shell and a non-conductingsphere is calculated in higher space dimensionN It is shown that as the space dimension increasesup to N = 9 the electrostatic energy ofthe two geometries decreases and beyond N = 9it increases Furthermore we discuss a simpleexample which illustrates classical renormalizationin electrostatics in higher dimensionsEnergy and Momentum Considerations in an Infinite Solenoidhttp://blogs.najah.edu/staff/al-jaber/article/Energy-and-Momentum-Considerations-in-an-Infinite-SolenoidPublished Articles Sami M AL-Jaber Department of Physics An-Najah National University Nablus West-Bank Palestine EMail:Jaber@najahedu On sabbatical leave: Palestine Technical UniversityPTU Kadoorie Tulkarm palestine Abstract: The electromagnetic linear momentum and the energy balance in an infinite solenoid with a time-dependant current are examined We show that the electromagnetic linear momentum density and its associated force density are balanced by the hidden momentum density and its associated hidden force density respectively We also show that exactly half the energy delivered by the power supply appears as stored magnetic energy inside the solenoid The other half is lost against the induced electromotive force that appears in the windings of the solenoid during the time through which the current is building up towards its final value This energy loss which is found in other analogue situations is necessary to transfer the system from an initial non-equilibrium state to a final equilibrium one A confined Hydrogen Atom in Higher Space Dimensionshttp://blogs.najah.edu/staff/al-jaber/article/A-confined-Hydrogen-Atom-in-Higher-Space-DimensionsPublished ArticlesAuthors: Muzayan Shaqoor and Sami M AL-Jaber Abstract: We compute ground state energies for the N-dimensional hydrogen atom confined in an impenetrable spherical cavity The obtained results show their dependence on the size of the cavity and the space dimension N We also examine the value of the critical radius of the cavity in different dimensions Furthermore the number of bound states was found for a given radius S in different space dimensionsconsideration from non-equilibrium to equilibrium state in the process of charging a capacitorhttp://blogs.najah.edu/staff/al-jaber/article/consideration-from-non-equilibrium-to-equilibrium-state-in-the-process-of-charging-a-capacitorPublished Articles A calculation of the energy loss due to a transition from non-equilibrium to equilibrium state in the process of charging a capacitor is given In this study it is shown that half of the total energy produced by the battery should be consumed in one form or another to reach the equilibrium state regardless of the values of the resistance and capacitance Degenerate electron gas and star stabilization in D dimensionshttp://blogs.najah.edu/staff/al-jaber/article/Degenerate-electron-gas-and-star-stabilization-in-D-dimensionsPublished Articles The quantum-mechanical energy the Fermi energy and the degeneracy pressure are derived for a degenerate Fermi gas in D spatial dimensions in Harmonic Oscillator In An Infinite N- Dimensional Spherical well http://blogs.najah.edu/staff/al-jaber/article/Harmonic-Oscillator-In-An-Infinite--N--Dimensional-Spherical-well-Published ArticlesAbstract The boundary effects on a quantum system are discussed by examining an N- dimensional harmonic oscillator confined in an impenetrable spherical well The corrections due to the boundary and the space dimension to the ground- state energy and wave function are calculated by using a linear approximation method which is linear in energy and by numerical method using mathematica Our results for the energy corrections obtained by the two methods are in very good agreement A simple analytical expression for the asymptotic dependence of the ground state energy on the well radius and on the dimension N is derived Finally the pressure needed to compress a free N-dimensional harmonic oscillator to a certain size is computed Ideal Bose Gas in Higher Dimensionshttp://blogs.najah.edu/staff/al-jaber/article/Ideal-Bose-Gas-in-Higher-DimensionsPublished Articles Some physical properties of the behavior of an ideal non- relativistic Bose gas in N dimensional space are theoretically investigated The general analytic expressions of the critical temperature T c of Bose Einstein condensation and the high- temperature behavior of the gas have been derived The dependence of these physical quantities on space dimension is discussed and some numerical values are calculated Moreover the limit of these quantities in the infinite dimensional space N is also examined A Confined N-Dimensional Harmonic Oscillatorhttp://blogs.najah.edu/staff/al-jaber/article/A-Confined-N-Dimensional-Harmonic-OscillatorPublished Articles Abstract We compute the energy eigenvalues for the N -dimensional harmonic oscillator confined in an impenetrable spherical cavity The results show their dependence on the size of the cavity and the space dimension N The obtained results are compared with those for the free N -dimensional harmonic oscillator and as a result the notion of fractional Strongly Singular Potentials in One Dimensionhttp://blogs.najah.edu/staff/al-jaber/article/Strongly-Singular-Potentials-in-One-DimensionPublished ArticlesAbstract: Strongly singular potentials are analyzed in one dimension namely the nth derivative of a delta function potentialConnection between the spectrum and the moments of the ground-state density in N-dimensional spacehttp://blogs.najah.edu/staff/al-jaber/article/Connection-between-the-spectrum-and-the-moments-of-the-ground-state-density-in-N-dimensional-spacePublished ArticlesAbstract We show that a series of recurrent inequalities derived in N = 3 have the same formal expressions in any dimension N 2 They are derived from the multipole sum rules and provide us with upper bounds for the moments of the ground-state density depending only on the lowest multipole excitation energy These bounds are transformed into approximate recurrent relations by means of an empirical correction factor The 1r potential and the harmonic oscillator play a key role in establishing this factor which is exact for these two potentials by construction For a large class of potentials we show that this factor tends to 1 as N In such cases at the large-N limit the lowest state for each multipole excitation exhausts the sum rule It thus acquires the characteristics of the one-phonon excitation typical of the harmonic oscillator PACS numbers: 0365w 0365Ge 0230Hq Planck's Spectral Distribution Law in N Dimensions http://blogs.najah.edu/staff/al-jaber/article/Plancks-Spectral-Distribution-Law-in-N-Dimensions-Published ArticlesAbstractPlancks spectral distribution law is derived in N-dimensional space Some relevant formulas are thus obtained and analyzed The behavior of these formulas in higher dimensions is examined and some numerical values are calculatedSome aspects of an infinite N-dimensional spherical potential wellhttp://blogs.najah.edu/staff/al-jaber/article/Some-aspects-of-an-infinite-N-dimensional-spherical-potential-wellPublished ArticlesAbstract: We consider the solution of Schrodinger equation in N dimensions for the infinite N-dimensional spherical potential well Some aspects of the radial part and the angular part of the wave function are presented and discussed In particular the effective potential orthonormality energy eigenvalues and the degeneracy are investigated Thus the role of the topological structure of the configuration space of a physical system on the quantum nature of the system is emphasizedHarmonic oscillator in an impenetrable spherical wellhttp://blogs.najah.edu/staff/al-jaber/article/Harmonic-oscillator-in-an-impenetrable-spherical-wellPublished ArticlesAbstract: The boundary effects on a quantum system are discussed by examining a harmonic oscillator in an impenetrable spherical well The boundary corrections to the ground-state energy and wave function are calculated via a linear approximation method which is linear in energy A simple analytical expression for the asymptotic dependence of the ground-state energy on the well radius is derivedPhotoionization of a One-Electron N-Dimensional Atom http://blogs.najah.edu/staff/al-jaber/article/Photoionization-of-a-One-Electron-N-Dimensional-Atom-Published ArticlesAbstractWe consider the photoionization of a one-electron atom in N-dimensional space and derive the total cross-section It is shown that depends strongly on the dimension N Thus we emphasize the role of the topological structure of a system on the physical properties of the systemGround-state energy of the N-dimensional two-electron atomshttp://blogs.najah.edu/staff/al-jaber/article/Ground-state-energy-of-the-N-dimensional-two-electron-atomsPublished ArticlesAbstract: In this paper we derive an expression for the first-order energy correction to the ground-state of two-electron atoms in the N-dimensional space The expression yields the well-known result for the three-dimensional space It is also shown that the value of the correction decreases as N increases and it vanishes as N goes to infinityThe second derivative of a delta- function potential: http://blogs.najah.edu/staff/al-jaber/article/The-second-derivative-of-a-delta--function-potential-Published ArticlesAbstract: We consider an exactly solvable model namely the interaction that is one of the point interactions For the repulsive case we drive the reflection and transmission coefficients It is shown that the coefficients satisfy the unitarity of the scattering matrix If the incident particle has a certain energy then the barrier becomes perfectly reflective Furthermore it is shown that the barrier becomes completely transmittive for the high-energy behavior For the attractive case we examine both the bound states and the scattering states It is shown that there exist two bound states and for the scattering case it is demonstrated that one recovers the same reflection and transmission coefficients that were obtained for the repulsive caseEnergy consideration in the two-capacitor problemhttp://blogs.najah.edu/staff/al-jaber/article/Energy-consideration-in-the-two-capacitor-problemPublished ArticlesAbstract A derivation of the specific electrostatic energy loss for two interacting capacitors is given The connecting wires are assumed to be superconducting The method of derivation is based purely on the Poynting vector involved in the process without any reference to the nature of the mechanism that may be involved in achieving a final equilibrium stateN-Dimensional Bound States for an Inverse Fraction Power Potentialhttp://blogs.najah.edu/staff/al-jaber/article/N-Dimensional-Bound-States-for-an-Inverse-Fraction-Power-PotentialPublished Articlesتم حساب قيم الطاقة الصحيحة التامة ودوالها في البعد النوني N للجهد ذي الاس الكسري العكسي Vr = ?r-12 ur-32 تشير النتائج الى أن ثمة عدداً لا نهائياً من دوال حالات الربط وأن هذه الدوال قابلة للمعايرة إضافة إلى ذلك، فإن كل دالة من هذه الدوال تتضمن علاقة بين ? v وكمية الزخم الزاوي L والبعد NFermi Gas in D-Dimensional Space http://blogs.najah.edu/staff/al-jaber/article/Fermi-Gas-in-D-Dimensional-Space-Published ArticlesAbstractWe consider a Fermi gas in D-dimensional spaceand show how the physical properties of the systembehave as a function of the dimension D in particularthe density of states the Fermi energy and the radius of the Fermi hypersphereThe fine structure of the N-dimensional hydrogen atomhttp://blogs.najah.edu/staff/al-jaber/article/The-fine-structure-of-the-N-dimensional-hydrogen-atomPublished ArticlesAbstract: The fine structure of energy levels of a hydrogen atom in N dimensions is given This is done by calculating the first-order energy corrections due to the relativistic correction to kinetic energy spin-orbit coupling and Darwin term Thus we emphasize the role of the topological structure of the configuration space of a physical system on the quantum nature of an observable of the systemHydrogen Atom in N Dimensions http://blogs.najah.edu/staff/al-jaber/article/Hydrogen-Atom-in-N-Dimensions-Published ArticlesSome aspects of the N-dimensional hydrogen atomare discussed The complete solution for the energyeigenfunctions is presented and the radial distributionfunction is examined Degeneracy of energy levels expectation values 1r and1r2 and the virial theorem areconsidered It is shown that the effect of the effectivepotential manifests itself in some of the aspects beinginvestigated International Journal of Theoretical Physics Volume 37 Number 4 April 1998 On the radial- part equation of the wave function in N dimensionshttp://blogs.najah.edu/staff/al-jaber/article/On-the-radial--part-equation-of-the-wave-function-in-N-dimensionsPublished ArticlesAbstract: We consider the equation for the radial part of the wave function of the Schrodinger equation in the N-dimensional space A new effective potential is derived when the equation for the radial part of the wave function is written in the form of a one-dimensional Schrodinger equation As a constructive example we find and discuss the solution the orthonormality and the energy eigenvalues of the radial part of the wave function for an infinite spherical potential well in N dimensionsQuantization of Angular Momentum in the N-Dimensional Spacehttp://blogs.najah.edu/staff/al-jaber/article/Quantization-of-Angular-Momentum-in-the-N-Dimensional-SpacePublished ArticlesAbstract: We consider the most general case of the quantization of angular momentum in the N-dimensional space We show that a hydrogen atom when viewed in an N-dimensional multiply connected space the angular momentum must be N-12-integralOrigin of the Darwin Termhttp://blogs.najah.edu/staff/al-jaber/article/Origin-of-the-Darwin-TermPublished ArticlesAbstract: The Darwin term is shown to be of a magnetic origin It is derived from the non-relativistic dynamics of a magnetic dipole moving in an external electric field The underlying effect is closely related to spin-orbit couplingDecay of the Charged Harmonic Oscillatorhttp://blogs.najah.edu/staff/al-jaber/article/Decay-of-the-Charged-Harmonic-OscillatorPublished ArticlesAbstract: We apply the Van Kampen-Steinwedel principal axis transformation to the problem of finding time-dependent probability distributions for decaying states of the harmonic oscillator The result lends itself easily to computer simulation Results for the decay of 1 2 and 15 are givenMomentum Conservation in the Aharonov-Casher Effecthttp://blogs.najah.edu/staff/al-jaber/article/Momentum-Conservation-in-the-Aharonov-Casher-EffectPublished ArticlesAbstract: In the Aharonov-Casher effect the neutron exerts a non-vanishing force on a static line of charge a charged wire The reaction of this force is the time rate of change of the electromagnetic momentumMomentum Conservation in the Aharonov-Bohm Effecthttp://blogs.najah.edu/staff/al-jaber/article/Momentum-Conservation-in-the-Aharonov-Bohm-EffectPublished ArticlesAbstract: In the Aharonov-Bohm effect the electron exerts a non-vanishing force on the flux whisker The reaction of this force is the time rate of change of the electromagnetic momentumTopological Considerations in Quantum Theoryhttp://blogs.najah.edu/staff/al-jaber/article/Topological-Considerations-in-Quantum-TheoryPublished ArticlesAbstract: We consider the most general case of the restricted rigid rotor controlled by passive mechanical devices at The purpose of theses devices is to restrict the particles motion to a domain of a covering space 0M where M is an odd integer This system which is not a Hamiltonian one on the physical space 0 2 is compared with a Hamiltonian system having delta function barriers at The case of M is even integer is also discussed by using only one mechanical device at =0 This non-Hamiltonian system is compared with a Hamiltonian system having a delta function barrier at =0 It is shown that many of the wave functions of the non-Hamiltonian system are the same as those of the Hamiltonian ones with an average reflection coefficient of 1M1 for odd M and 2M for even M which are the classical values We show how in the case of very large M the superposition principle leads to the de Broglie resonancesRecipient of PFDP Teaching Excellence Award 2010http://blogs.najah.edu/staff/al-jaber/article/Recipient-of-PFDP-Teaching-Excellence-Award-2010General PostsOn July 26th 2010 Professor Sami Al-Jaber from the Department of Physics at the University has been selected as the recipient of the PFDP Teaching Excellence Award for the year 2010 Professor Al-Jaber was a professor of Theoretical Physics and the Dean of Graduate Studies between 2002-2004 at An-Najah Dean of the Faculty of Science 2004-2007 and Dean of Scientific Research between 2007-2009 He was also granted An-Najah Research Award in 2007 He obtained a PhD in Theoretical Physics from the Southern Illinois University Carbondale Illinois USA in august 1991Editorial Board member - Journal of Modern Physics (JMP)http://blogs.najah.edu/staff/al-jaber/article/Editorial-Board-member---Journal-of-Modern-Physics-JMPGeneral PostsProf Sami M AL-Jaber - Editorial Board member for Journal of Modern physics JMPClassical Electrodynamics II 422522 Spring 2009. Projectshttp://blogs.najah.edu/staff/al-jaber/article/Classical-Electrodynamics-II--422522--Spring-2009-ProjectsGeneral Posts1 Ruba M Saeed: Energy loss of charged particles in collisions Chapter 13: Sec 131 end of sec 134 2 Ruwida F Dweeckat: Energy loss of charged particles in collisions Chapter 13: sec 135 end of chapter 3 Fadi F Taher: Relativistic particles in EM fields Chapter 12: Sec 121 end of sec 125 4 Mursi A Arda: Radiation damping Chapter 16: Sec 161 end of sec163 NOTES: 1 Each student must submit a maximum of 7 typed pages of hisher project 2 Due date for submission is Thursday April 10 2009 3 Each must make a presentation for 20 minutesOn going Researchhttp://blogs.najah.edu/staff/al-jaber/article/On-going-ResearchOn Going ResearchesCurrent Research: Prof Sami AL-Jaber Department of Physics The current research interest is in quantum confined systems for different kind of potentials The simple harmonic oscillator is a topic of utmost importance on quantum mechanics It is applicable in different physical situations and has the great advantage that has a closed form solutions for energy eigenvalues and eigen functions Various investigations of the harmonic oscillator has been considered the time-dependent harmonic oscillator harmonic oscillator with point interaction relativistic harmonic oscillator an-harmonic oscillator and the spiked harmonic oscillator Recently there has been some renewed interest in confined systems like the hydrogen atom and harmonic oscillator This interest is highly motivated by the technological advances in the filed of semiconductor quantum dots where the computations of electronic structure of such systems necessarily has to take into account the presence of finite boundaries on the system The purpose here is to extend the isotropic harmonic oscillator plus a central potential N dimensions Selected cases of the form of the central potential needs further work The motivations behind this proposed work is due to its interest in atomic and molecular physics One can also apply this work to psedo potentials in higher dimensions which is useful in nuclear physics I addition this is of great interest to mathematicians and physicists in theories studying so-called supper spaces or sipper-manifolds This is related to Clifford analysis which allows for an elegant formulation of higher dimensional theories