Gabel, Fabian Nuraddin AlexanderFabian Nuraddin AlexanderGabelGallaun, DennisDennisGallaunGroßmann, Julian PeterJulian PeterGroßmannLindner, MarkoMarkoLindnerUkena, RikoRikoUkena2021-11-012021-11-012021-10-18arXiv: 2110.09339 (2021)http://hdl.handle.net/11420/10707We 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.enMathematics - Spectral TheoryMathematics - Spectral TheoryComputer Science - Numerical AnalysisMathematical PhysicsMathematics - Mathematical PhysicsMathematics - Numerical Analysis65J10, 47B36 (Primary) 47N50 (Secondary)MathematikFinite sections of periodic Schrödinger operatorsPreprint10.48550/arXiv.2110.093392110.09339v1Preprint