We study discrete Schr\"odinger operators $H$ with periodic potentials as they are typically used to approximate aperiodic Schr\"odinger 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 $H_n$. For integer-valued potentials, we show that the finite section method is applicable as soon as H is invertible. This statement remains true for $\{0, \lambda\}$-valued potentials with fixed rational $\lambda$ and period less than nine as well as for arbitrary real-valued potentials of period two.

翻译：我们研究的是具有定期潜力的离散 Schr\'doninger操作员,因为通常用于接近像Fibonacci Hamiltonian这样的周期性Schr\'odinger操作员。我们证明这是对有限区段方法适用性的有效测试,这一程序通过增加有限的平方次母体约合H美元。对于整数价值的潜力,我们表明,只要H是不可倒置的,有限区段方法就适用。对于固定合理的$\lambda$和少于9年的固定区段和任意实际价值的2年潜力来说,这一说明仍然有效。