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The shifted -l expansion technique (SLET) has been developed to solve for the eigenvalues of Schrödinger equation in three (3D) and two dimensions (2D). SLET simply consists of using 1/l as a perturbation parameter, wherel = l − β. β is a suitable shift, l is the angular momentum quantum number for the 3D-case, l = |m| for the 2D-case, and m is the magnetic quantum number. Unlike the shifted large -N expansion theory (SLNT), SLET seems to be applicable to a wider number of problems of significant interest in physics.

The asymptotic iteration method is used for Dirac and Klein-Gordon equations with a linear scalar potential to obtain the relativistic eigenenergies. A parameter, ς = 0, 1, is introduced in such a way that one can obtain Klein-Gordon bound states from Dirac bound states. It is shown that this method asymptotically gives accurate results for both Dirac and Klein-Gordon equations.

The asymptotic iteration method is applied, to calculate the angular spheroidal

Diagonal and transition magnetic moments of the negative parity, spin-1/2 heavy baryons are studied in framework of the light cone QCD sum rules. By constructing the sum rules for different Lorentz structures, the unwanted contributions coming from negative (positive) to positive (negative) parity transitions are removed. It is obtained that the magnetic moments of all baryons, except Λ 0 b , Σ + c and Ξ ′+ c , are quite large. It is also found that the transition magnetic moments between neutral negative parity heavy Ξ ′0 Q and Ξ 0 Q baryons are very small. Magnetic moments of the Σ Q → Λ Q and Ξ ′± Q → Ξ ± Q transitions are quite large and can be measured in further experiments.

Linear and nonlinear optical absorption coefficients of the two-dimensional semiconductor ring in the perpendicular magnetic field B are calculated within independent electron approximation. Characteristic feature of the energy spectrum are crossings of the levels with adjacent nonpositive magnetic quantum numbers as the intensity B changes. It is shown that the absorption coefficient of the associated optical transition is drastically decreased at the fields corresponding to the crossing. Proposed model of the Volcano disc allows to get simple mathematical analytical results, which provide clear physical interpretation. An interplay between positive linear and intensity-dependent negative cubic absorption coefficients is discussed; in particular, critical light intensity at which additional resonances appear in the total absorption dependence on the light frequency is calculated as a function of the magnetic field and levels' broadening.