Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912129021378560 |
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| author | Akramov, M. Trunk, C. Yusupov, J. Matrasulov, D. |
| author_facet | Akramov, M. Trunk, C. Yusupov, J. Matrasulov, D. |
| contents | We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and derivation of secular equation for arbitrary quantum graphs is presented. Application of the approach for the star graph is demonstrated by obtaining eigenfunctions and eigenvalues explicitely. Practical application of the model in conducting polymers and branched molecular chains is discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_14397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice Akramov, M. Trunk, C. Yusupov, J. Matrasulov, D. Quantum Physics Mesoscale and Nanoscale Physics We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and derivation of secular equation for arbitrary quantum graphs is presented. Application of the approach for the star graph is demonstrated by obtaining eigenfunctions and eigenvalues explicitely. Practical application of the model in conducting polymers and branched molecular chains is discussed. |
| title | Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2411.14397 |