Investigation of Fermions in Non-commutative Space by Considering Kratzer Potential

The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.     

AIM Solutions to the DKP Equation for Spin-1 Particles in the Presence of Kratzer Potential in (2+1) Dimensions

The relativistic Duffin–Kemmer–Petiau equation for spin-1 particles in the presence of the Kratzer potential is studied analytically within the framework of the asymptotic iteration method. The exact energy eigenvalues and corresponding eigenfunctions of spin-1 particles are obtained for arbitrary quantum states by solving the Duffin–Kemmer–Petiau equation with Kratzer potential.     

Effect of the dielectric-constant mismatch and magnetic field on the binding energy of hydrogenic impurities in a spherical quantum dot

Within the effective mass approximation and variational method the effect of dielectric constant mismatch between the size-quantized semiconductor sphere, coating and surrounding environment on impurity binding energy in both the absence and presence of a magnetic field is considered. The dependences of the binding energy of a hydrogenic on-center impurity on the sphere and coating radii, alloy concentration, dielectric-constant mismatch, and magnetic field intensity are found for the GaAs–Ga_1−xAl_xAs–AlAs (or vacuum) system.     

Ground states of the hydrogen molecule and its molecular ion in the presence of a magnetic field using the variational Monte Carlo method

ABSTRACT

By using the variational Monte Carlo (VMC) method, we calculated the 1sσ_g-state energies, the dissociation energies, and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0 and 10?a.u. The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of a magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of the VMC method can be successfully extended to cover the case of molecules under the effect of a magnetic field.     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

Bound state solution of the Klein-Gordon equation for vector and scalar Hellmann plus modified Kratzer potentials

In this study, the analytical solutions of the Klein–Gordon equation for any l states of the scalar and vector Hellmann plus modified Kratzer potential are derived by using an approximation method to the centrifugal potential term. The analytical expressions for eigenvalues and corresponding normalized eigenfunctions of the spin-zero particle have been estimated by using the parametric Nikiforov-Uvarov method. The solution for the radial part of the Klein-Gordon equation is formulated in terms of the generalized Jacobi polynomials. The energy state equation and the wave function for special cases are in good agreement with the previous literature. In addition, we have measured the numerical results of the energy eigenvalues and also the trend of the eigenvalues concerning of different potential parameters have been plotted. Furthermore, it was shown that the energy levels E and quantum numbers n and l are inversely proportional to each other.     

Perturbative approach to the hydrogen atom in a strong magnetic field

We consider states of the hydrogen atom with the principal quantum number n≤3 and zero magnetic quantum number in a constant homogeneous magnetic field ?. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n³?/?₀～5, where ?₀ is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.     

Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength

We compute, via a variational mixed-base method, the energy spectrum of a two-dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find that the relativistic spectrum does not present s states.     

Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit

We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term κ. We also investigate the energy eigenvalues of the Dirac particles for the well-known Kratzer-Fues and modified Kratzer potentials which are Mie-type potentials.     

The effects of pressure and hydrogenic donor impurity on the linear and nonlinear optical properties of a GaAs/GaAlAs nanowire superlattice

The combined effects of hydrostatic pressure, presence and absence of hydrogenic donor impurity are investigated on the linear and nonlinear optical absorption coefficients and refractive index changes of a GaAs/Ga_1−xAl_xAs nanowire superlattice. The wave functions and corresponding eigenvalues are calculated using finite difference method in the framework of effective mass approximation. Analytical expressions for the linear and third order nonlinear optical absorption coefficients and refractive index changes are obtained by means of compact-density matrix formalism. The linear and third order nonlinear absorption coefficient and refractive index changes are presented as a function of photon energy for different values of hydrostatic pressure, incident photon intensity and relaxation time in the presence and absence of hydrogenic donor impurity. It is found that the linear and third order nonlinear absorption coefficients, refractive index changes and resonance energy are quite sensitive to the presence of impurity and applied hydrostatic pressure. Moreover, the saturation in optical spectrum and relaxation time can be adjusted by increasing pressure in presence of impurity whereas the effect of hydrostatic pressure is negligible in the case of absence of hydrogenic impurity.     

Impurity effects on the magnetization and magnetic susceptibility of an electron confined in a quantum ring under the presence of an external magnetic field

The magnetization and the magnetic susceptibility of a single electron confined in a two-dimensional (2D) parabolic quantum ring under the effect of external uniform magnetic field and in the presence of an acceptor impurity have been studied. The shifted 1/N expansion method was used to solve the Hamiltonian quantum ring within the effective mass approximation. The computed energy spectra, the magnetization and magnetic susceptibility have been displayed as a function of the quantum ring parameters: confinement strength ω₀, magnetic field strength (ω_c), and temperature (T). The obtained energy results show level-crossings, in the absence and presence of acceptor impurity, which are manifested as oscillations in the magnetization and magnetic susceptibility curves.     

Effects of surface nonlinear interactions on the local critical behavior

The energy spectrum and the wave functions of quantum wells in strong magnetic fields parallel to the potential walls are calculated analytically by means of a new, graph supported method. This Arrow Train Method allows to solve the recurrence relations which originate in the evaluation of eigenvalue determinants of infinite order. The energy eigenvalues for infinite barrier height are computed as a power series in the magnetic fieldB and the center of orbit coordinatez ₀. The power series is evaluated up to the 18th order inB ² for the first four levels and for cyclotron radii comparable to or considerable less than the well width. The corresponding wave functions and the field dependent center of mass shifts are obtained.Work supported in part by the Deutsche Forschungsgemeinschaft     

Realization of the Spectrum Generating Algebra for the Generalized Kratzer Potentials

The dynamical symmetries of the Kratzer-type molecular potentials (generalized Kratzer molecular potentials) are studied by using the factorization method. The creation and annihilation (ladder) operators for the radial eigenfunctions satisfying quantum dynamical algebra SU(1,1) are established. Factorization method is a very simple method of calculating the matrix elements from these ladder operators. The matrix elements of different functions of r, r\fracddrr\frac{d}{dr}, their sum Γ₁ and difference Γ₂ are evaluated in a closed form. The exact bound state energy eigenvalues E _n,ℓ and matrix elements of r, r\fracddrr\frac{d}{dr}, their sum Γ₁ and difference Γ₂ are calculated for various values of n and ℓ quantum numbers for CO and NO diatomic molecules for the two potentials. The results obtained are in very good agreement with those obtained by other methods.     

Compressibility and collisional effects on thermal instability of a partially ionized medium

The thermal instability of a finitely conducting hydromagnetic composite and compressible medium is studied to include the frictional effects with neutrals. The effect of compressibility is found to be stabilizing. In contrast to the nonoscillatory modes for (C _p/g)β > 1 in the absence of a magnetic field;C _v, β andg being specific heat at constant pressure, uniform adverse temperature gradient and acceleration due to gravity respectively, the presence of magnetic field introduces oscillatory modes in the system. The overstable case is also discussed. The magnetic field is found to have a stabilizing effect on the system for (C _p/g)β > 1.     

Thermodynamic and magnetic properties of the electron gas in the inhomogeneous magnetic field Hr−1

The nonrelativistic and relativistic energy eigenvalues of the electron in the inhomogeneous magnetic fieldH _z =Hr ⁻¹,r=(x ² +y ²)^1/2 are derived in a form displaying the explicit spin dependence. The possibility of magnetic hydrogen atom formation and the spontaneouse ⁺ e ⁻ pair creation following from these eigenvalues is mentioned. The expressions for pressure, energy, particle number and magnetic moment of an electron gas in this IMF are calculated in the degenerate limit. The possibility of spontaneous magnetisation,i.e., ferromagnetic behaviour, is established. Further, the pressure of the electron gas in the same type of fields is an order of magnitude higher than those in a homogeneous magnetic field and crossed homogeneous electric and magnetic fields for comparable field strengths.     

The magnetic properties across the martensitic transition in the Co38Ni34Al28 alloy

The magnetic properties of the Co₃₈Ni₃₄Al₂₈ alloy have been studied. The alloy exhibits a first order austenite-martensite phase transition in the temperature region between 155 and 247 K. A strain of 0.07% is produced across this phase transition. The Arrott plots obtained from the isothermal magnetic field dependence of magnetization indicate the presence of spontaneous magnetization both in the austenite and martensite phases, confirming the ferromagnetic character of the alloy up to room temperature. The temperature dependence of the high field magnetization indicates the presence of spin wave excitations, spin wave excitation gap and spin wave-spin wave interactions in the martensite phase. The magnetic anisotropy energy constant for the Co₃₈Ni₃₄Al₂₈ alloy is estimated both with the help of the standard law of approach to saturation of magnetization, and also from the field dependence of magnetization using the field for technical saturation of magnetization. The temperature dependences of these energy terms are compared. The estimated values of the magnetic anisotropy constant seem to be in agreement with the magnitude of the spin wave excitation gap estimated from the temperature dependence of high field magnetization.     

Thermodynamic properties and the approximate solutions of the Schrödinger equation with the shifted Deng–Fan potential model

With the introduction of a new improved approximation scheme (Pekeris-type approximation) to deal with the centrifugal term, the energy eigenvalues and the wave functions of the Schrödinger equation of the shifted Deng–Fan molecular potential are obtained, via the asymptotic iteration method. Rotational–vibrational energy eigenvalues of some diatomic molecules are presented, these results are in good agreement with other results in the literature. For these selected diatomic molecules, energy eigenvalues obtained are in much better agreement with the results obtained from the rotating Morse potential model for moderate values of rotational and vibrational quantum numbers. Furthermore, thermodynamic properties such as the vibrational mean U, specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues are studied.     

Bianchi Type V magnetized string dust cosmological models with Petrov-type degenerate

Bianchi Type V massive string cosmological models with free gravitational field of Petrov Type degenerate in the presence of magnetic field with variable magnetic permeability are investigated. The magnetic field is due to an electric current produced along the x-axis. The F ₂₃ is the only non-vanishing component of electromagnetic field tensor F _ij . Maxwell’s equations F _[ij;k] = 0 and F _;j ^ij = 0 are satisfied by F ₂₃ = constant. The behaviour of the model in the presence and absence of magnetic field and other physical aspects are also discussed.      

Screening effect on the binding energies of shallow donors,acceptors and excitons in finite-barrier quantum wells

The conduction and valence subband energies in the presence of an electric field are calculated using the fifth-order Runge–Kutta method. The binding energies of shallow donors, acceptors and excitons in finite-barrier GaAs/Ga_1−xAl_xAs quantum wells are then obtained variationally in the presence of a magnetic field. The effects of a spatially dependent screening function ϵ (r) on the calculation of binding energies are specifically investigated. The use of ϵ (r) in comparison with the use of a constant ϵ₀increases the binding energy of acceptors as the increase on shallow donors and excitons is quite small.