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A duality between Schroedinger operators on graphs and certain Jacobi matrices

Pavel Exner
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Abstract

The known correspondence between the Kronig-Penney model and certain Jacobi matrices is extended to a wide class of Schroedinger operators on graphs. Examples include rectangular lattices with and without a magnetic field, or comb-shaped graphs leading to a Maryland-type model.

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Pavel Exner. 1995-09-01. A duality between Schroedinger operators on graphs and certain Jacobi matrices. https://arxiv.org/abs/funct-an/9509002

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