A quantum pseudodot system with two-dimensional pseudoharmonic oscillator in external magnetic and Aharonov-Bohm fields

Using the Nikiforov–Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field inside dot and Aharonov–Bohm (AB) field inside a pseudodot. The exact solutions for energy eigenvalues and wave functions are computed as functions of the chemical potential parameters, applied magnetic field strength, AB flux field, magnetic quantum number and temperature. Analytical expression for the light interband absorption coefficient and absorption threshold frequency are found as functions of applied magnetic field and geometrical size of quantum pseudodot. The temperature dependence energy levels for GaAs semiconductor are also calculated.     

Optical properties of a donor impurity in a two-dimensional quantum pseudodot

We investigate the linear and nonlinear optical properties of a donor impurity confined by a two-dimensional pseudoharmonic potential both including harmonic dot and antidot potentials in the presence of a strong magnetic field. Calculations are made by using the perturbation method and the compact density-matrix approach within the effective-mass approximation. Based on the computed energies and wave functions, the linear, third-order nonlinear and total optical absorption coefficients as well as the refractive index changes have been examined. The results are presented as a function of the incident photon energy for the different values of the chemical potential of the electron gas and the zero point of the pseudoharmonic potential. The results show that the optical properties of a donor impurity in a two-dimensional pseudoharmonic QD are strongly affected by the zero point of the pseudoharmonic potential, the chemical potential of the electron gas and the Coulomb interaction.     

Topological and non inertial effects on the interband light absorption

In this work, we investigate the combined influence of the nontrivial topology introduced by a disclination and non inertial effects due to rotation, in the energy levels and the wave functions of a noninteracting electron gas confined to a two-dimensional pseudoharmonic quantum dot, under the influence of an external uniform magnetic field. The exact solutions for energy eigenvalues and wave functions are computed as functions of the applied magnetic field strength, the disclination topological charge, magnetic quantum number and the rotation speed of the sample. We investigate the modifications on the light interband absorption coefficient and absorption threshold frequency. We observe novel features in the system, including a range of magnetic field without corresponding absorption phenomena, which is due to a tripartite term of the Hamiltonian, involving magnetic field, the topological charge of the defect and the rotation frequency.     

The relativistic bound states of a non-central potential

We investigate the relativistic effects of a moving particle in the field of a pseudoharmonic oscillatory ring-shaped potential under the spin and pseudospin symmetric Dirac wave equation. We obtain the bound-state energy eigenvalue equation and the corresponding two-components spinor wave functions by using the formalism of supersymmetric quantum mechanics (SUSYQM). Furthermore, the non-relativistic limits are obtained by simply making a proper replacement of parameters. The thermodynamic properties are also studied. Our numerical results for the energy eigenvalues are also presented.     

Effect of magnetic field on electron spectrum and probabilities of intraband quantum transitions in spherical quantum-dot-quantum-well

The effect of magnetic field on electron energy spectrum, wave functions and probabilities of intraband quantum transitions in multilayered spherical quantum-dot-quantum-well (QDQW) CdSe/ZnS/CdSe/ZnS is studied. Computations are performed in the framework of the effective mass approximation and rectangular potential barriers model. The wave functions are expanded over the complete basis of functions obtained as exact solutions of the Schrodinger equation for the electron in QDQW without the magnetic field.It is shown that magnetic field takes off the spectrum degeneration with respect to the magnetic quantum number and changes the localization of electron in the nanostructure. The field stronger effects on the spherically-symmetric states, especially in the case of electron location in the outer potential well. The magnetic field changes more the radial distribution of probability of electron location in QDQW than the angular one. The oscillator strengths of intraband quantum transitions are calculated as functions of the magnetic field induction and their selection rules are established.     

1/<Emphasis Type="Italic">Q</Emphasis> expansion for the energy spectrum of quantum dots

A new method is proposed for calculating the energy spectrum and the wave functions of N-electron quantum dots with an arbitrary confining potential. The method consists in expansion with respect to a dimensionless quantum parameter 1/Q, which is expressed in terms of the ratio of the characteristic Coulomb energy of electron-electron interaction to the characteristic energy of one-particle transition in a confining potential. Two-electron quantum dots with a parabolic confining potential in an external magnetic field are considered. Strongly correlated states of the system and the spin rearrangement in a strong magnetic field are analyzed. Analytic expressions are obtained for the energy and the wave functions of the system. It is shown that restriction of the analysis only to the first three terms in the quantum-parameter expansion gives an accuracy of one percent when calculating the energy even for values of Q on the order of unity, i.e., for the presently implementable GaAs quantum dots. The expressions for energy obtained are in a good agreement with the experimental data for quantum dots in a perpendicular magnetic field.     

Exact Solutions of the Duffin-Kemmer-Petiau Equation with a Pseudoharmonic Potential in the Presence of a Magnetic Field in (1+2) Dimensions

We will consider the relativistic Duffin-Kemmer-Petiau equation in the presence of a pseudoharmonic potential in a magnetic field in the (1+2)-dimensional space-time for spin-one particles. To derive the energy eigenvalues and corresponding eigenfunctions, the analytical Nikiforov-Uvarov Method is used and some explanatory figures are included.     

Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential

Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin–orbit coupling quantum number κ. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy between members of the pseudospin doublet is removed by tensor interaction. Furthermore, the radial node structure of the Dirac spinor is discussed.     

Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential

In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding wave functions are also deduced.     

Relativistic solutions for diatomic molecules subject to pseudoharmonic oscillator in arbitrary dimensions

The exact solutions of the N-dimensional Klein-Gordon equation in the presence of an exactly solvable potential of V(r)=De(r/re-re/r)2 type have been obtained. The N dimensional Klein-Gordon equation has been reduced to a first-order differential equation via Laplace transformation. The exact bound state energy eigenvalues and corresponding wave functions for CH,H2,and HCl molecules interacting with pseudoharmonic oscillator potential in the arbitrary N dimensions have been determined. Bound state eigenfunctions used in applications related to molecular spectroscopy are obtained in terms of confluent hypergeometric functions.     

Two-particle correlations on a 1D lattice in a constant magnetic field

The problem of two particles interacting through the Hubbard potential on a 1D finite lattice in a constant uniform magnetic field is solved. Exact wave functions are determined, and an equation for the energy spectrum is constructed and analyzed. The possibility of a field-induced singlet-triplet transition is demonstrated.     

Weakly bound electrons in an external magnetic field

The electron behavior in a spherical symmetric potential well in the presence of an external magnetic field is studied. The transcendental equation for the energy spectrum is derived. The energy of the bound state is approximately calculated. The electron wave function and the probability current are found.     

Impurity states of electrons in quantum dots in external magnetic fields

The influence of isolated impurity atoms on the electron energy spectrum in a parabolic quantum dot in quantizing magnetic field is studied. The impurity potential is approximated by a Gaussian separable operator which allows one to obtain the exact solution of the problem. We demonstrate that in the electron energy spectrum there is a set of local levels which are split from the Landau zone boundaries in the upward or downward direction depending on the impurity type. We have calculated the local level positions, the wave functions of electrons in bound states, and the residues of the electron scattering amplitudes by impurity atoms at the poles.     

Electronic states in a cylindrical quantum dot with the modified Pöschl-Teller potential in the presence of external magnetic field

Energy levels of an electron in a cylindrical quantum dot with a modified Pöschl-Teller potential in the presence of external homogeneous magnetic field are studied. Analytical expressions for the wave function and energy of the particle are obtained. Different regimes of magnetic quantization are considered and peculiarities of behavior of the electron energy spectrum depending on the value of applied magnetic field are revealed.     

Optical absorption and refractive index of a donor impurity in a three-dimensional quantum pseudodot

The optical absorption and refractive index of a donor impurity confined by a three-dimensional quantum pseudodot are studied using the matrix diagonalization method within the effective-mass approximation. The great advantage of our methodology is that it enables us to tune confinement strength and regime by varying two parameters in the model potential. Based on the computed energies and wave functions, the linear, third-order nonlinear and total optical absorption coefficients as well as the refractive index changes have been examined. The results are presented as a function of the incident photon energy for the different values of the chemical potential of the electron gas and the zero point of the pseudoharmonic potential. We find that the larger optical nonlinearity will be obtained by varying the zero point of the pseudoharmonic potential compared to the chemical potential of electron gas.     

Approximate solution of the Schrödinger equation for an atom in the field of a standing wave

We present an approximate method of calculation of energy spectrum and wave functions of translational motion of a two-level atom in the field of a standing wave at zero value of the quasimomentum. Wave functions in the momentum representation are expressed in terms of confluent hypergeometric functions in case of continuous spectrum and in terms of Hermitian polynomials in case of discrete spectrum. The energy spectrum exhibits infinite compaction at transition from discrete part to continuous, as it is the case for, e.g., Coulombian potential.     

Linear and nonlinear optical properties in a disk-shaped quantum dot with a parabolic potential plus a hyperbolic potential in a static magnetic field

Linear and nonlinear optical properties in a disk-shaped quantum dot (DSQD) with a parabolic potential plus a hyperbolic potential in a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron are obtained by three kinds of approximation methods. It is found that optical absorption coefficients and refractive index changes are not only by the characteristic parameters of the hyperbolic potential and the confinement frequency, but also by the magnetic field.     

Linear and nonlinear intersubband optical absorption in a disk-shaped quantum dot with a parabolic potential plus an inverse squared potential in a static magnetic field

The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.     

Thermodynamic properties of the XX model in a chain with a period two and three coupling

The exact solutions for the energy spectrum of the XX model with a periodic coupling and an external transverse magnetic field h are obtained. The diagonalization procedure is discussed, and analytical and numerical solutions are given. Using the solutions for period-two coupling, the free energy, entropy, and specific heat are calculated as functions of temperature and applied transverse external magnetic field. Their expressions show that below a particular value v and above a value u of the magnetic field |h|, the entropy and the specific heat vanish exponentially in the low temperature limit.     

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form . The energy eigenvalues and eigenfunctions of the bound-states for the Schr?dinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.