Gabel, FabianFabianGabelGallaun, DennisDennisGallaunGroßmann, JulianJulianGroßmannLindner, MarkoMarkoLindnerUkena, RikoRikoUkena2024-01-242024-01-242023In: Choi, Y., Daws, M., Blower, G. (eds) Operators, Semigroups, Algebras and Function Theory. IWOTA 2021. Operator Theory: Advances and Applications, vol 292. Birkhäuser, Cham. (2023)https://hdl.handle.net/11420/45281We 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.enBook part10.1007/978-3-031-38020-4_6Other