The paper is devoted to Schrödinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the Lax-Phillips scattering theory the asymptotic behaviour of the phase shift is investigated in detail and its relation to the spectral shift is discussed. In particular, the trace formula and the Birman-Krein formula are verified directly. The results ...

This paper intends to study the following degenerate fractional Schrödinger–Kirchhoff–Poisson equations with critical nonlinearity and electromagnetic fields in R3: {ε2sM([u]s,A2)(−Δ)Asu+V(x)u+ϕu=k(x)|u|r−2u+(Iμ∗|u|2s♯)|u|2s♯−2u,x∈R3,(−Δ)tϕ=u2,x∈R3, where ε>0 is a positive parameter, 3/4<s<1, 0<t<1, V an electric potential satisfying suitable assumptions, 0<k∗≤k(x)≤k∗, Iμ(x)=|x|3−μ 0<μ<3, 2s♯=3...

As an important model in quantum semiconductor devices, the Schrödinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical op...

We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an H4-regular solution, a first-order error bound in the H1 norm is shown and used to derive a second-order error bound in the L2 norm. For the cubic Schrödinger equation with an H4-regular solution, first-order convergence in the H2 norm is used to obtain s...