The varying-mass Schrödinger equation (VMSE) has been successfully applied to model electronic properties of semiconductor hetero-structures, for example, quantum dots and quantum wells. In this paper, we consider VMSE with small random heterogeneities, and derive a radiative transfer equation as its asymptotic limit. The main tool is to systematically apply the Wigner transform in the classical regime when the rescaled Planck constant $ϵ\ll 1$, and expand the Wigner equation to proper orders of ϵ. As a proof of concept, we numerically compute both VMSE and its limiting radiative transfer equation, and show that their solutions agree well in the classical regime.

变质量Schrödinger方程（VMSE）已成功应用于模型化半导体异质结构的电子特性，例如量子点和量子阱。在本文中，我们考虑具有较小随机异质性的VMSE，并推导了一个辐射传递方程作为其渐近极限。当重新缩放普朗克常数时，主要工具是在经典状态下系统地应用Wigner变换$ϵ\ll \mathrm{1个}$，扩大维格纳方程的正确顺序ε。作为概念证明，我们对VMSE及其极限辐射传递方程进行了数值计算，并表明它们的解在经典体系中吻合良好。