The application of adiabatic method for the description of impurity states in quantum nanostructures

Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

“…The elaborated methods, symbolic-numerical algorithms (SNAs) and programs [23][24][25][26][27][28][29][30][31][32][33][34][35] can be applied for solving the BVPs of discrete and continuous spectra of the Schrödinger-type equations and the analysis of spectral and optical characteristics of QWs, QWr's and QD's in external fields, as well as the spectra of models of deformed nuclei [41].…”

“…The models with nonzero values of these parameters were announced in [8,25]. Throughout the paper we make use of the reduced atomic units [2,5]:…”

“…In our ear-lier work we elaborated the calculation schemes, symbolic-numerical algorithms (SNAs) and programs, based on the generalized Kantorovich method (KM) for numerical solving with required accuracy the boundary-value problems (BVPs) of discrete and continuous spectra describing the axial-symmetric models of quantum wells(QWs), quantum wires(QWrs) and quantum dots(QDs) in external fields within the framework of the effective mass approximation [23][24][25][26][27][28][29][30][31][32][33][34][35]. Meanwhile, for the analysis and estimations of the appropriate range of material parameters, spectral and optical characteristic of quantum dots at the first stage of investigation, conventionally, approximate eigenvalues and eigenfunctions evaluated in the analytical form were applied [6-8, 14, 22].…”

“…Meanwhile, for the analysis and estimations of the appropriate range of material parameters, spectral and optical characteristic of quantum dots at the first stage of investigation, conventionally, approximate eigenvalues and eigenfunctions evaluated in the analytical form were applied [6-8, 14, 22]. However, it is a real challenge to specify the range of applicability of such approximations in the problems, depending on a few parameters [2], e.g., for impurity states of quantum wires in a homogeneous magnetic field [25].…”

Direct Interband Light Absorption in Conical Quantum Dot

“…The Hamiltonian of the fast subsystem includes variables as parameters of the slow subsystem, and an effective potential energy plays a slow subsystem (parametrically depending on coordinates of slow system) energy fast [14][15][16]. This peculiar method of separation of variables allows us to give an analytical description of single-particle states.…”