Spectral Instability for Some Schroedinger Operators
  We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schroedinger operators in one dimension, and apply it to the complex resonances of a typical operator with a dilation analytic potential. 
A. Aslanyan and E. B. Davies