Fourier method for one dimensional Schr\"odinger operators with singular periodic potentials
Plamen Djakov, Boris Mityagin
TL;DR
This paper introduces a Fourier-based approach utilizing quasi-derivatives to analyze the spectral properties of one-dimensional Schrödinger operators with singular periodic potentials.
Contribution
It develops a novel Fourier method specifically designed for Schrödinger operators with singular periodic potentials, advancing spectral analysis techniques.
Findings
Effective spectral analysis of singular periodic potentials
New Fourier method using quasi-derivatives
Potential applications in quantum physics
Abstract
By using quasi--derivatives, we develop a Fourier method for studying the spectral properties of one dimensional Schr\"odinger operators with periodic singular potentials.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Differential Equations and Boundary Problems · Advanced Mathematical Modeling in Engineering