Abstract: Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.
Abstract: In a major nuclear accident, the released fission products (FPs) and the structural materials are likely to influence the transport of iodine in the reactor coolant system (RCS) of a pressurized water reactor (PWR). So far, the thermodynamic data on cesium and silver species used to estimate the magnitude of FP release show some discrepancies, data are scarce and not reliable. For this reason, it is crucial to review the thermodynamic values related to cesium and silver materials. To this end, we have used state-of-the-art quantum chemical methods to compute the formation enthalpies and entropies of AgHMoO₄, CsHMoO₄, and AgCsMoO₄ in the gas phase. Different quantum chemical methods have been investigated (DFT and CCSD(T)) in order to predict the geometrical parameters and the energetics including the correlation energy. The geometries were optimized with TPSSh-5%HF method, followed by a single point calculation of the total electronic energies using the CCSD(T) wave function method. We thus propose with a final uncertainty of about 2 kJmol⁻¹ standard enthalpies of formation of AgHMoO₄, CsHMoO₄, and AgCsMoO₄.
Abstract: The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.
Abstract: Electrical conduction in a quasi-one-dimensional
polycrystalline metallic ring with a long electron phase coherence
length realized at low temperature is investigated. In this situation, the
wave nature of electrons is important in the ring, where the electrical
current I can be induced by a vector potential that arises from a static
magnetic field applied perpendicularly to the ring’s area. It is shown
that if the average grain size of the polycrystalline ring becomes
large (or comparable to the Fermi wavelength), the electrical current
I increases to ~I0, where I0 is a current in a disorder-free ring. The
cause of this increasing effect is examined, and this takes place if the
electron localization length in the polycrystalline potential increases
with increasing grain size, which gives rise to coherent connection
of tails of a localized electron wave function in the ring and thus
provides highly coherent electrical conduction.
Abstract: Annihilations, phase shifts, scattering lengths and
elastic cross sections of low energy positrons scattering from
magnesium atoms were studied using the least-squares variational
method (LSVM). The possibility of positron binding to the
magnesium atoms is investigated. A trial wave function is suggested
to represent e+-Mg elastic scattering and scattering parameters were
derived to estimate the binding energy and annihilation rates. The
trial function is taken to depend on several adjustable parameters, and
is improved iteratively by increasing the number of terms. The
present results have the same behavior as reported semi-empirical,
theoretical and experimental results. Especially, the estimated
positive scattering length supports the possibility of positronmagnesium
bound state system that was confirmed in previous
experimental and theoretical work.
Abstract: In this article, a new method is proposed for the measuring of well-being inequality through a model composed of superimposing satisfaction waves. The displacement of households’ satisfactory state (i.e. satisfaction) is defined in a satisfaction string. The duration of the satisfactory state for a given period is measured in order to determine the relationship between utility and total satisfactory time, itself dependent on the density and tension of each satisfaction string. Thus, individual cardinal total satisfaction values are computed by way of a one-dimensional form for scalar sinusoidal (harmonic) moving wave function, using satisfaction waves with varying amplitudes and frequencies which allow us to measure wellbeing inequality. One advantage to using satisfaction waves is the ability to show that individual utility and consumption amounts would probably not commute; hence, it is impossible to measure or to know simultaneously the values of these observables from the dataset. Thus, we crystallize the problem by using a Heisenberg-type uncertainty resolution for self-adjoint economic operators. We propose to eliminate any estimation bias by correlating the standard deviations of selected economic operators; this is achieved by replacing the aforementioned observed uncertainties with households’ perceived uncertainties (i.e. corrected standard deviations) obtained through the logarithmic psychophysical law proposed by Weber and Fechner.
Abstract: Supersymmetric Quantum Mechanics is an interesting
framework to analyze nonrelativistic quantal problems. Using these
techniques, we construct a family of strictly isospectral Hulth´en
potentials. Isospectral wave functions are generated and plotted for
different values of the deformation parameter.
Abstract: The energy-level structure of a pair of electron and positron confined in a quasi-one-dimensional nano-scale potential well has been investigated focusing on its trend in the small limit of confinement strength ω, namely, the Wigner molecular regime. An anisotropic Gaussian-type basis functions supplemented by high angular momentum functions as large as l = 19 has been used to obtain reliable full configuration interaction (FCI) wave functions. The resultant energy spectrum shows a band structure characterized by ω for the large ω regime whereas for the small ω regime it shows an energy-level pattern dominated by excitation into the in-phase motion of the two particles. The observed trend has been rationalized on the basis of the nodal patterns of the FCI wave functions.
Abstract: We demonstrate that it is possible to compute wave function normalization constants for a class of Schr¨odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P in decimals.
Abstract: We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.
Abstract: The solvated electron is self-trapped (polaron) owing
to strong interaction with the quantum polarization field. If the
electron and quantum field are strongly coupled then the collective
localized state of the field and quasi-particle is formed. In such a
formation the electron motion is rather intricate. On the one hand the
electron oscillated within a rather deep polarization potential well
and undergoes the optical transitions, and on the other, it moves
together with the center of inertia of the system and participates in
the thermal random walk. The problem is to separate these motions
correctly, rigorously taking into account the conservation laws. This
can be conveniently done using Bogolyubov-Tyablikov method of
canonical transformation to the collective coordinates. This
transformation removes the translational degeneracy and allows one
to develop the successive approximation algorithm for the energy and
wave function while simultaneously fulfilling the law of conservation
of total momentum of the system. The resulting equations determine
the electron transitions and depend explicitly on the translational
velocity of the quasi-particle as whole. The frequency of optical
transition is calculated for the solvated electron in ammonia, and an
estimate is made for the thermal-induced spectral bandwidth.
Abstract: The wave function at the origin is an important quantity in studying many physical problems concerning heavy quarkonia. This is because that it is using for calculating spin state hyperfine splitting and also crucial to evaluating the production and decay amplitude of the heavy quarkonium. In this paper, we present the variational method by using the single-parameter wave function to estimate the WFO for the ground state of heavy mesons.
Abstract: Many recent high energy physics calculations
involving charm and beauty invoke wave function at the origin
(WFO) for the meson bound state. Uncertainties of charm and beauty
quark masses and different models for potentials governing these
bound states require a simple numerical algorithm for evaluation of
the WFO's for these bound states. We present a simple algorithm for
this propose which provides WFO's with high precision compared
with similar ones already obtained in the literature.