The work discusses a numerical WKB-method use for the approximation of a high oscillating solution of a stationary Schr-odinger equation. An integral occurs WKB approximation that should be computed by means of spectral methods. Thereby, it will be investigated how the use of spectral methods, in this work the Clenshaw-Curtis quadrature and barycentric interpolated antiderivative after expansion in a chebyshev series, effects the global error of the WKB-Method in comparison with other quadrature methods (such as the simpson quadrature or trapezoidal rule). Therefore, in chapter 3, the error estimation of the WKB-method will be extended by one estimation of the error, that arises during the numerical calculation of the occurring phase integral. Furthermore, in the chapters 4 and 5, the WKB-method and the integration, with, former mentioned, spectral methods will be discussed based on two numerical examples.