Non-self-adjoint boundary-value problem with discontinuous density function

We determine spectrum and principal functions of the non-self-adjoint differential operator corresponding to 1-D non-self-adjoint Schrodinger equation with discontinuous density function, provide some sufficient conditions guaranteeing finiteness of eigenvalues and spectral singularities, and introduce the convergence properties of principal functions. Copyright (C) 2009 John Wiley & Sons, Ltd.