Discrete Schrödinger equation on graphs: An effective model for branched quantum lattice
M. AkramovNational University of Uzbekistan named after Mirzo Ulugbek, Tashkent, UZBEKISTANCarsten TrunkInstitute for Mathematics, Technische Universität Ilmenau, Ilmenau, Thüringen, GERMANYJambul YusupovKimyo International University in Tashkent, Tashkent, Tashkent, UZBEKISTAND. MatrasulovTurin Polytechnic University in Tashkent, Tashkent, Tashkent, UZBEKISTAN
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Annotatsiya
Abstract We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of the discrete Schrödinger equation that is used to write the solution for quantum graphs. The formulation of the problem and derivation of secular equation for arbitrary quantum graphs is presented. The application of the approach for the star graph is demonstrated by obtaining eigenfunctions and eigenvalues explicitely. The practical application of the model in conducting polymers and branched molecular chains is discussed.
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