Pseudomodes for Schrodinger operators with complex potentials

For one-dimensional Schrodinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. We develop a first systematic non-semi-classical approach, which results in a substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous ones. Applications of the present results to higher-dimensional Schrodinger operators are also discussed. (C) 2018 Elsevier Inc. All rights reserved.