We consider discrete Schr\"odinger operators with aperiodic potentials given by a Sturmian word, which is a natural generalisation of the Fibonacci-Hamiltonian. We introduce the finite section method, which is often used to solve operator equations approximately, and apply it first to periodic Schr\"odinger operators. It turns out that the applicability of the method is always guaranteed for integer-valued potentials. By using periodic approximations, we find a necessary and sufficient condition for the applicability of the finite section method for aperiodic Schr\"odinger operators and a numerical method to check it.

翻译：我们考虑的离散的Schr\'odinger操作员具有由Sturmian单词给出的定期潜力,这是Fibonacci-Hamiltonian的自然概括。我们引入了有限部分方法,该方法通常用于大致解析操作员方程式,并首先适用于定期的Schr\'odinger操作员。结果发现,该方法的适用性总是对整值潜能值的保证。通过使用定期近似,我们找到了对定期Schr\\'odian操作员适用有限部分方法的一个必要和充分的条件,以及进行校验的数字方法。