Lorentzian path integral for quantum tunneling and WKB approximation for wave-function

Recently, the Lorentzian path integral formulation using Picard-Lefschetz theory has attracted much attention in quantum cosmology. In this paper, we analyze tunneling amplitude mechanics by and compare it with WKB analysis of conventional Schr\"{o}dinger equation. We show that is consistent approximation for wave-function Euclidean utilizing solutions constraint also consider some problems discuss a simpler semiclassical without integrating lapse function.