The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables, similarly as in the solution of the Vlasov-Poisson system by means of the Bernstein-Greene-Kruskal method. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed and shown to be immediately integrable up to a recursive chain of quadratures in position space only. As it stands, the treatment of the self-consistent, Wigner-Poisson system is beyond the scope of the method, which assumes a given smooth time-independent external potential. Accuracy tests for the series expansion are also provided. Examples of anharmonic potentials are worked out up to a high order on the quantum diffraction parameter.

一维固定量子Vlasov方程使用能量作为动力学变量之一进行分析，类似于通过Bernstein-Greene-Kruskal方法求解Vlasov-Poisson系统的问题。在量子隧穿效应很小的半经典情况下，开发了无限级数解，并且证明了该解可以立即积分到仅在位置空间中的正交递归链上。就目前而言，对自洽的Wigner-Poisson系统的处理超出了该方法的范围，该方法假定给定的平滑时间独立外部势能。还提供了系列扩展的准确性测试。在量子衍射参数上高阶地计算出非谐电位的实例。