Werner Kirsch and Stanislav Molchanov Random Schroedinger Operators with Potentials Having Stationary Increments (131K, LaTeX 2e) ABSTRACT. We study one dimensional Schr\"{o}dinger operators $H_{\omega}=-\frac{d^{2}% }{dx^{2}}+V_{\omega}$ where $V_{\omega}$ is a stochastic process with stationary, independent increments.