Schrödinger Operators with Thin Spectra

The determination of the spectrum of a Schrödinger operator is a fundamental problem in mathematical quantum mechanics. We discuss a series of results showing that Schrödinger operators can exhibit spectra that are remarkably thin in the sense of Lebesgue measure and fractal dimensions. We begin with a brief discussion of results in the periodic theory, and then move to a discussion of aperiodic models with thin spectra.

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