Bounds for Schrödinger operators on the half-line perturbed by dissipative barriers

Abstract

We consider Schrödinger operators of the form $H_R=-d^2/d{x}^2+q+i\gamma {\chi }_{[0,R]}$ for large $R>0$, where $q\in L^1(0,\infty )$ and $\gamma >0$. Bounds for the maximum magnitude of an eigenvalue and for the number of eigenvalues are proved. These bounds complement existing general bounds applied to this system, for sufficiently large $R$.

18 pages, 2 figures, Accepted in Integral Equations and Operator Theory