One can generate certain special solutions to the one-dimensional Schr\"odinger equation, exp[±iS_±(x)], such that S_±(x) and derivatives are computationally unique, slowly varying, and do not have oscillatory or steplike behavior associated with the de Broglie wavelength. This leads to a method for accurate numerical solution which has all the advantages of high computational speed and conceptual simplicity of the JWKB approximation---of which it is the extension to an exact solution.
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Newman et al. (1972) studied this question.