http://ir.dspu.edu.ua/jspui/handle/123456789/124 2026-10-04T18:57:35Z http://ir.dspu.edu.ua/jspui/handle/123456789/11802 Название: THE INFLUENCE OF QUANTUM DOT GEOMETRY ON HOLE ENERGY SPECTRA WITHIN THE FRAMEWORK OF THE LUTTINGER MODEL Авторы: Лешко, Роман Ярославович; Білинський, Ігор Васильович; Лешко, Ольга Володимирівна; Монастирський, Тарас Романович Краткий осмотр (реферат): We present a theoretical study of the hole energy spectra and wave-function spatial distributions in spherical, cubic, and conical GaAs/AlAs quantum dots. The calculations are performed within the four-band Luttinger–Kohn model using a three-dimensional plane- wave expansion method, which allows for the exact analytical evaluation of the Hamiltonian matrix elements via the Fourier transforms of the nanostructure shape functions. We demonstrate that the reduction of spatial confinement symmetry from spherical to cubic and conical geometries alters the energy levels structure by taking off the characteristic four-fold and six-fold degeneracies into lower-symmetry multiplets. Cross-sectional distribution of probability density reveal that the hole states exhibiting distinct S-and P-like characteristics by a mixing of heavy- and light-hole components. Furthermore, a comparative analysis at a constant internal volume shows a blue-shift of the ground state energy confirming that geometric shapes with sharp boundaries minimize the effective carrier volume and significantly enhance quantum confinement. 2026-09-01T00:00:00Z http://ir.dspu.edu.ua/jspui/handle/123456789/11745 Название: METHODOLOGICAL APPROACHES TO THE USE OF GOOGLE COLABORATORY IN THE PRACTICAL TRAINING OF STUDENTS Авторы: SHAKLEINA, Iryna Краткий осмотр (реферат): The article summarizes the practical experience of using Google Colaboratory in the educational process at different educational levels. The technical advantages of the environment are evident: no installation required access to computing resources, native integration with Google Classroom and Google Drive, and support for teamwork. The author proposes a methodological model for organizing practical work in the Colab environment, demonstrating the structure’s versatility across various subject areas, from the basics of programming in secondary education institutions to data analysis and artificial intelligence systems in higher education institutions. The limitations of the free platform tariff are identified, and methods to compensate for them are proposed. Описание: У статті узагальнено практичний досвід використання Google Colaboratory в освітньому процесі на різних рівнях освіти. Очевидними є технічні переваги цього середовища: відсутність потреби в інсталяції, доступ до обчислювальних ресурсів, нативна інтеграція з Google Classroom і Google Drive, а також підтримка командної роботи. Автор пропонує методичну модель організації практичної роботи в середовищі Colab, демонструючи універсальність її структури для різних предметних галузей — від основ програмування в закладах середньої освіти до аналізу даних і систем штучного інтелекту у вищих навчальних закладах. Визначено обмеження безкоштовного тарифу платформи та запропоновано способи їх подолання. 2026-09-01T00:00:00Z http://ir.dspu.edu.ua/jspui/handle/123456789/11716 Название: Exciton States in Spherical Non-Concentric Core–Shell Quantum Dots Авторы: Лешко, Роман Ярославович; Лешко, Ольга Володимирівна; Білинський, Ігор Васильович; Карпин, Дмитро Степанович Краткий осмотр (реферат): The electronic and excitonic structure of non-concentric CdSe/CdS core-shell spherical quantum dots is investigated theoretically, with the core rigidly displaced from the shell center. Hole states are computed within the four-band Luttinger–Kohn model expanded in a plane-wave basis, with the displaced-core confining potential treated exactly, and exciton states are obtained by configuration interaction including the direct electron-hole Coulomb attraction and the short-range exchange interaction. The displacement reduces the confining symmetry from spherical to axial and lifts the degeneracy of the band-edge hole multiplet, yielding a fine-structure splitting that increases monotonically with the core offset. The same mechanism reshapes the exciton spectrum: the ground-state transition undergoes a blueshift as the core approaches the shell boundary, while the exchange-induced dark–bright splitting grows steadily with displacement. The calculated absorption edge is in quantitative agreement with the experimentally measured value. This agreement is obtained only when excitonic effects are included, with the electron-hole Coulomb attraction supplying the redshift required to reconcile theory and experiment. The results identify the core displacement as an effective structural degree of freedom for tuning both the emission energy and the exciton fine structure of colloidal core-shell nanocrystals. 2026-08-01T00:00:00Z http://ir.dspu.edu.ua/jspui/handle/123456789/11715 Название: Енергетичний спектр електрона в розділених та злитих сферичних квантових точках Авторы: Лешко, Роман Ярославович; Лешко, Ольга Володимирівна; Білинський, Ігор Васильович; Мельник, Ярослав Юрійович; Очеретяний, Андрій Олександрович; Чекін, Олександр Іванович; Квик, Марко Володимирович Краткий осмотр (реферат): We present a highly efficient semi-analytical approach to model electronic states in fused spherical quantum dots by deriving an exact analytical Fourier transform of their 3D shape function using cylindrical Bessel functions. This mathematical novelty allows the direct application of the plane-wave expansion method to solve the Schrödinger equation with a spatially dependent effective mass, completely eliminating the need for resource-intensive 3D spatial meshing. Applying this to a GaAs/AlGaAs heterostructure, we demonstrate that strong geometric overlap induces robust quantum-mechanical hybridization, causing an exponential splitting of degenerate energy levels into symmetric and antisymmetric states. The model guarantees an exact asymptotic transition to isolated quantum dot solutions, providing a fast and rigorous tool for prototyping complex nanostructures. 2026-09-01T00:00:00Z