2018/08/24 by Peter Howard, Alim Sukhtayev, Howard, Peter +1
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1808.08264
Working with a general class of linear Hamiltonian systems on [0, 1], we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated with appropriately chosen paths of Lagrangian subspaces of ℂ2n. We verify that our applicability class includes Dirac and Sturm-Liouville systems, as well as a system arising from differential-algebraic equations for which the spectral parameter appears nonlinearly.