| Bibliography: | References -- 2 Mathematical aspects of physical properties of nanostructures -- 2.1 Introduction -- 2.1.1 Energy band gap -- 2.1.1.1 Mathematical formulations -- 2.1.2 Dielectric constant -- 2.1.3 Debye temperature -- 2.1.3.1 Analytical formulation -- 2.1.4 Photoelectric properties -- 2.2 Conclusion -- References -- 3 Theoretical methods for physical characterization of nanostructures -- 3.1 Introduction -- 3.2 Density functional theory and its applications -- 3.2.1 Fundamentals of density functional theory -- 3.2.2 Applications in material science -- 3.2.2.1 Structural optimization |