Exciton in a quantum-well structure for arbitrary magnetic field strengths

Fine structure of excitons in a quantum well in the presence of a nonhomogeneous magnetic field

“…The in-plane Hamiltonian [H 2D (r e , r h )] describes the electron and hole motion in the xy plane in a nonhomogeneous magnetic field, which is represented by the vector potential A(r). We will make use of a variational approach 19 to assume that the difference between the 2D and 3D Coulomb interactions [W (r, z e,h )] can be made very small by the choice of an optimum value for γ, 20 which is a variational parameter that is calculated from the average of W (r, z e,h ) over the exciton wave function. The perpendicular contribution [H ⊥ (z e,h )] describes the exciton confinement in the quantum well, i.e., in the z direction, which is not affected by the magnetic field.…”

“…For a complete description of the dependence of the γ parameter with the quantum well width and also with an applied homogeneous magnetic field (which is negligible in the weak field regime) we refer to Ref. [19].…”

The Energy States of Excitons in a Harmonic Quantum Dot

“…The coexistence of the Coulombic and harmonic potential terms in the relative Hamiltonian makes the exact analytic solution not possible and difficult to treat theoretically by conventional methods, such as perturbation technique, because these two terms could be comparable in magnitude. Most theoretical works study only the properties of this exciton Hamiltonian in two limits, namely, strong and weak confinement regimes [2,17,18].…”

2D H-Atom in an Arbitrary Magnetic Field via Pseudoperturbation Expansions Through the Quantum Number l

“…In almost most of problems concerning such structures the eigenspectrum of the 2D-Schrődinger equation is investigated. For example, the 2D hydrogenic energy levels in a constant magnetic field of arbitrary strength has been a subject of numerous theoretical and experimental investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”