Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field

We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.

Spin symmetry in the relativistic modified Rosen-Morse potential with the approximate centrifugal term

By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated twocomponent spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case a →0.

Continuum states of modified Morse potential

Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrodinger equation for the modified Morse potential. The normalised analytical radial wave functions are presented, and a corresponding calculation formula of phase shifts is derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some numerical results are calculated to show the accuracy of our results.

Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass

The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

Binding energy of the donor impurities in GaAs-Ga_(1-x)Al_xAs quantum well wires with Morse potential in the presence of electric and magnetic fields

The behavior of a donor in the GaAs–GaAlAs quantum well wire represented by the Morse potential is examined within the framework of the effective-mass approximation. The donor binding energies are numerically calculated for with and without the electric and magnetic fields in order to show their influence on the binding energies. Moreover, how the donor binding energies change for the constant potential parameters(De, re, and a) as well as with the different values of the electric and magnetic field strengths is determined. It is found that the donor binding energy is highly dependent on the external electric and magnetic fields as well as parameters of the Morse potential.

The bound state solution for the Morse potential with a localized mass profile

We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.

The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method

We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.

Wave Functions for Time-Dependent Morse Potentials

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

Nonrelativistic quantum effects of the Lorentz symmetry violation on the Morse potential

We search for Lorentz symmetry violation effects at low-energy regime by exploring the Dirac equation in(1+1)-dimensions and the possibility of dealing with quantum systems with spherical symmetry.We bring a discussion about the influence of the Lorentz symmetry violation effects on the spectrum of molecular vibrations caused by the coupling between a fixed vector field and the derivative of the fermionic field.Further,we discuss the influence of this Lorentz symmetry violation background on the revival time.

Scattering States of l-Wave Schr¨odinger Equation with Modified Rosen–Morse Potential

Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.

Solution of the Schrodinger equation for a particular form of Morse potential using the Laplace transform

In this paper, we have solved the Schrdinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the Laplace transform technique which reduces the second-order differential equation to a first-order.

Morse Potential in the Momentum Representation

The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a nodeless function and the mutual orthogonality of functions is ensured by the phase functions arg[（p）], It is interesting to see that the [~ （p）[ is symmetric with respect to the axis p = 0 and the number of wave crest of [ （p）[ is equal to n ＋ 1. We also study the variation of ]k（p）l with respect to . The arnplitude of ｜ψ（p）] first increases with the quantum number n and then deceases. Finally, we notice that the discontinuity in phase occurs at some points of the momentum p and the position and momentum probability densities are symmetric with respect to their arguments.

The Mechanical Properties of Skutterudite CoAs_3 by Molecular Dynamics(MD) Simulation

Skutterudite CoAs3 is a potentially important thermoelectric material. Morse potential is employed here to carry out molecular dynamics simulations of nanobulk CoAs3 at the temperature of 0 K. The stress-strain relationships under uniaxial tensile and/or compressive strain are obtained. The elastic modulus, extreme strength and deformation mechanism are studied. The simulation results indicate that nanobulk CoAs3 abruptly ruptures at much higher strain level under tension than conventional bulk CoAs3. Both the extreme stresses under tension and compression are much higher than those of conventional bulk CoAs3.

Theoretical Studies on Adsorption Sites and States of O and N on Ni(311)

The adsorption of O and N atoms on the Ni（311） surface was investigated by the 5-parameter Morse potential（5-MP） method in detail. For the O-Ni（311） system, there are three surface adsorption states and the fcc-3-fold site is metastable; the frequency of 75 meV[67 meV in high resolution electron energy loss spectroscopy（HREELS） experiment] is attributed to the vibration at the hcp-3-fold site. For the N-Ni（311） system, however, there are only two surface adsorption states（no surface adsorption state was calculated atfcc-3-fold site）. In addition, subsurface states were predicted and all critical characteristics were obtained for the two systems.

Systematic Approach to Compute the Vibrational Energy Levels of Diatomic Molecules

In continuation of our previous paper of the anharmonic potentials analysis through the Floquet representation, we performed in this work a systematic calculation of the diatomic vibrational energy levels as well as the corresponding wave functions. The solution of Schrödinger equation according to Morse potential, which is a suitable model to describe the diatomic vibrational spectra, has been introduced;thus the explicit formulas to the second order have been established. As an illustration, the dissociation energies of some molecules species (i.e. ScN, LiH, Cl2 and NO) have been computed, as well as the wave functions and the corresponding probability densities, relating to the (ScN) molecule have been represented. Comparisons of our results with those of literature have been made.

Molecular mechanics-based finite element analysis of graphene sheet and carbon nanotubes using the rebo potential

Molecular mechanics-based finite element(FE)models of graphene sheet and singlewalled zigzag and armchair carbon nanotubes(CNTs)are developed on the basis of the assumption that the carbon nanostructures,when loaded,behave like frame structures.The behavior of carbon–carbon bonds,which are represented by beam elements,is simulated using the many-body second generation reactive empirical bond order(REBO)potential.By means of the FE models,the tensile behavior of carbon nanostructures is simulated.The FE models are verified against molecular dynamics simulations.The computed results in terms of tensile stress–strain curves and fracture patterns are compared with results obtained using the pairwise modified-Morse potential.Different tensile properties and fracture patterns are predicted using the two potentials.This is mainly attributed to the deviations in the force–bond length curves and to the contribution of bond angle variation which is present in REBO.The present work is the first attempt to implement the REBO potential into a continuum model of carbon nanostructures and paves the way for a more systematic incorporation of atomistic simulation methods into continuum models.