arXiv ID: | 2110.09339v1 | Title: | Finite sections of periodic Schrödinger operators | Language: | English | Authors: | Gabel, Fabian Nuraddin Alexander ![]() Gallaun, Dennis Großmann, Julian Peter ![]() Lindner, Marko ![]() Ukena, Riko |
Keywords: | Mathematics - Spectral Theory; Mathematics - Spectral Theory; Computer Science - Numerical Analysis; Mathematical Physics; Mathematics - Mathematical Physics; Mathematics - Numerical Analysis; 65J10, 47B36 (Primary) 47N50 (Secondary) | Issue Date: | 18-Oct-2021 | Source: | arXiv: 2110.09339v1 (2021) | Abstract (english): | We study discrete Schrödinger operators H with periodic potentials as they are typically used to approximate aperiodic Schrödinger operators like the Fibonacci Hamiltonian. We prove an efficient test for applicability of the finite section method, a procedure that approximates H by growing finite square submatrices Hn. For integer-valued potentials, we show that the finite section method is applicable as soon as H is invertible. This statement remains true for {0, λ}-valued potentials with fixed rational λ and period less than nine as well as for arbitrary real-valued potentials of period two. |
URI: | http://hdl.handle.net/11420/10707 | Institute: | Mathematik E-10 | Document Type: | Preprint |
Appears in Collections: | Publications without fulltext |
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