On the spectrum of (non)magnetic Schrödinger operators - Miranda, Germán ; 0000-0003-2485-8055 (Centre for Mathematical Sciences, Lund University, 2025)
This thesis investigates the spectral properties of magnetic and nonmagnetic Schrödinger operators, which have applications in the distribution of superconductivity in type II superconductors and wave theory. The thesis begins with an introduction to the main results in the field, giving a more detailed presentation for clarity. Next, we focus on the original research articles conducted by the author in collaboration with others. We provide one of the first counterexamples in three dimensions to the monotonicity of the lowest eigenvalue of the magnetic Laplacian. The spectrum of the magnetic Laplacian is further analysed in general domains under a piecewise constant magnetic field and in the disc under a constant magnetic field. Lastly, we present a new approach to the comparison of eigenvalues of the Laplacian under different boundary conditions.