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Dynamical Symmetries for Nanostructures
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Group theoretical concepts elucidate fundamental physical phenomena, such as the spectrum of quantum systems and complex geometrical structures molecules and crystals. These concepts are extensively covered in numerous textbooks. The present monograph illuminates more subtle aspects featuring group theory for quantum mechanics, that is, the concept of dynamical symmetry. Dynamical symmetry groups complement the conventional groups: their elements induce transitions between states belonging to different representations of the symmetry group of the Hamiltonian. Dynamical symmetry appears as a hidden symmetry in the hydrogen atom and quantum rotator problem, but its main role is in nano and meso systems. Such systems include atomic clusters, large molecules, etc. They are expected to be the building blocks of quantum electronic devices and information transmitting algorithms. Elucidation of the electronic properties of such systems is facilitated by applying concepts of dynamical group theory.
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