The Cauchy problem with a rapidly oscillating initial condition for the homogeneous Schrödinger equation was studied in [5]. Continuing the research ideas of this work and [3], in this paper we construct the asymptotic solution to the following mixed problem for the nonstationary Schrödinger equation: L h u ≡ ih∂ t u + h 2 ∂ 2 x u − b(x, t)u = f (x, t), (x, t) ∈ Ω = (0, 1) × (0, T], u| t=0 = (x), u| x=0 = u| x=1 = 0, (1) where h > 0 is a Planck constant, u = u(x, t, h). b(x, t), f (x, t) ∈ C ∞ (¯ Ω), (x) ∈ C ∞ [0, 1] are given functions. The similar problem was studied in [7, 8] when the Plank constant is absent in the first term of the equation and asymptotics of solution of any order with respect to a parameter was constructed. In this paper, we use a generalization of the method used in