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Register a new userFinite section method for aperiodic Schrodinger operators
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Added by
Julian Grossmann
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We consider discrete Schrodinger 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 Schrodinger operators. It turns out that the applicability of the method is always guaranteed for integer-valued potentials provided that the operator is invertible. By using periodic approximations, we find a necessary and sufficient condition for the applicability of the finite section method for aperiodic Schrodinger operators and a numerical method to check it.
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