The independent solutions of the one-dimensional Schrödinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed numerical verification of the proposed approximation is performed for some exactly solvable problems arising from different kinds of potentials.
Vladimir V. Kudryashov. Yulian V. Vanne. "Explicit summation of the constituent WKB series and new approximate wave functions." J. Appl. Math. 2 (6) 265 - 275, 10 November 2002. https://doi.org/10.1155/S1110757X02112046