S S symmetry Review Theoretical Basis of Quantum-Mechanical Modeling of Functional Nanostructures Aleksey Fedotov 1,2 , Alexander Vakhrushev 1,2,*, Olesya Severyukhina 1,2, Anatolie Sidorenko 2 , Yuri Savva 2, Nikolay Klenov 3,4 and Igor Soloviev 3 1 Department Simulation and Synthesis Technology Structures, Institute of Mechanics, Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences, 426067 Izhevsk, Russia;
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[email protected] (O.S.) 2 Laboratory of Functional Nanostructures, Orel State University named after I.S. Turgenev, 302026 Orel, Russia;
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[email protected] (Y.S.) 3 Laboratory of Nanostructure Physics, Department of Microelectronics, Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia;
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[email protected] Abstract: The paper presents an analytical review of theoretical methods for modeling functional nanostructures. The main evolutionary changes in the approaches of quantum-mechanical modeling are described. The foundations of the first-principal theory are considered, including the stationery and time-dependent Schrödinger equations, wave functions, the form of writing energy operators, and the principles of solving equations. The idea and specifics of describing the motion and inter- action of nuclei and electrons in the framework of the theory of the electron density functional are Citation: Fedotov, A.; Vakhrushev, A.; Severyukhina, O.; Sidorenko, A.; presented. Common approximations and approaches in the methods of quantum mechanics are Savva, Y.; Klenov, N.; Soloviev, I.