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We study the influence of disorder on propagation of waves in one-dimensionalstructures. Transmission properties of the process governed by theSchr\"{o}dinger equation with the white noise potential can be expressedthrough the Lyapunov exponent $\gamma$ which we determine explicitly as afunction of the noise intensity \sigma and the frequency \omega. We finduniform two-parameter asymptotic expressions for $\gamma$ which allow us toevaluate $\gamma$ for different relations between \sigma and \omega. The valueof the Lyapunov exponent is also obtained in the case of a short-rangecorrelated noise, which is shown to be less than its white noise counterpart.

Lyapunov exponent of the random Schr\"{o}dinger operator with short-range correlated noise potential