On continuous movement of the discrete spectrum of Schrödinger operators

2018/04/25 by M. N. N. Namboodiri, Namboodiri, M. N. N., Sudhanshu Kumar +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #advanced mathematical theories #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1804.09560

Abstract

Continuous movement of discrete spectrum of the Schrödinger operator H(z)=-\fracd² dx²+V₀+z V₁, with ∫₀^∞ x |V_j(x)| dx < ∞, on the half-line is studied as z moves along a continuous path in the complex plane. The analysis provides information regarding the members of the discrete spectrum of the non-selfadjoint operator that are evolved from the discrete spectrum of the corresponding selfadjoint operator.

Related

• On traces and modified Fredholm determinants for half-line Schr "odinger\n operators with purely discrete spectra
• Thresholds and more bands of a.c. Spectrum for the discrete Schrödinger operator with a more general long range condition
• Discrete spectrum of Schrödinger operators with oscillating decaying potentials
• A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators
• Conditions for discreteness of the spectrum to Schr "odinger operator\n via non-increasing rearrangement, Lagrangian relaxation and perturbations