We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.
By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary m-state in two-dimensional Schrödinger wave equation with various power interaction potentials in constant magnetic and Aharonov–Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We calculate the energy levels of some diatomic molecules in the presence and absence of external magnetic and AB flux fields using different potential models. We found that the effect of the Aharonov–Bohm field is much as it creates a wider shift for m≠0 and its influence on m=0 states is found to be greater than that of the magnetic field. To show the accuracy of the present model, a comparison is made with those ones obtained in the absence of external fields. An extension to 3-dimensional quantum system have also been presented.
The dependence of the photoionization cross-section on photon energy is calculated for shallow donors in infinite-barrier GaAs/Ga1−xAlx As quantum well as a function of well width. The effect of a magnetic field is also considered.
The ground-state properties of a two-dimensional quantum-dot are studied. We have used the shifted 1/N expansion method to solve the relative part Hamiltonian of two electrons confined in a quantum in the presence of an applied uniform magnetic field. The spin singlet-triplet transition in the ground state of the QD is shown. We have also displayed the singlet-triplet energy gap, J = ∆ = ET – ES, against the strength of the magnetic field for two electron quantum dot. Based on comparisons, the eigenenergies obtained by the shifted method are in excellent agreement with exact, variational, Hartree-Fock (HF) and Full-Configuration Interaction (FCI) methods.