Module 1: Introduction
Milestones in nanoscience and nanotechnology, Nanostructures and quantum physics, Layered nanostructures and superlattices, Nanoparticles and nanoclusters, Carbon-based nanomaterials. Waveparticle duality: Blackbody radiation, interaction of radiation with matter, photoelectric effect, Compton effect, wave-particle duality, De-Broglie’s hypothesis, uncertainty relations, wave function, Schrodinger equation, Operators.
Module 2: Solutions of Schrodinger Equations
One-dimensional potential: Free electron in vacuum, electron in a potential well with infinite barriers, finite barriers and propagation of an electron above the potential well, Tunnelling: propagation of an electron in the region of a potential barrier. Three-dimensional potential: Electron in a rectangular potential well (quantum box) and spherically-symmetric potential well, Quantum harmonic oscillators, Phonons.
Module 3: Approximate methodsof finding quantum states:
Stationary perturbation theory for a system with non-degenerate states and degenerate states. Non-stationary perturbation theory, quasiclassical approximation.
Module 4: Quantum states in atoms and molecules:
Quantum states in hydrogen atom, emission spectrum, spin of an electron. Many-electron atoms: wave function of a system of identical particles, hydrogen molecule
Module 5: Quantization in nanostructures:
Number and density of quantum states, low-dimensional structures, Quantum states of an electron in low-dimensional structures, density of states for nanostructures, Double-quantum-dot structures (artificial molecules), electron in a periodic one-dimensional potential, onedimensional superlattice of quantum dots, three-dimensional superlattice of quantum dots.