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Reflections on the almost Mathieu operator

Integral Equations and Operator Theory, ISSN: 0378-620X, Vol: 28, Issue: 1, Page: 45-59
1997
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Article Description

An explicit derivation of a tridiagonal matrix form for the almost Mathieu operator (Harper's equation) is obtained via conjugation with a reflection operator, valid for all rational values of the rotation parameter. The difference between even and odd values of the denominator is highlighted. This tridiagonal form is useful for numerical eigenvalue computations; some Matlab code is included.

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