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A new technique was recently developed to approximate the solution of theSchroedinger equation. This approximation (dubbed ERS) is shown to yield abetter accuracy than the WKB-approximation. Here, we review the ERSapproximation and its application to one and three-dimensional systems. Inparticular, we treat bound state solutions. We further focus on randompotentials in a quantum wire and discuss the solution in the context ofAnderson localization.

ERS approximation for solving Schr\"odinger's equation and applications