This paper is devoted to developing and analysing a highly accurate conservative method for solving the quantum Zakharov system. The scheme is based on a linearly-implicit compact finite difference discretization and conserve the mass as well as energy in discrete level. Detailed numerical analysis is presented which shows the method is fourth-order accurate in space and second-order accurate in time. Several numerical examples are reported to confirm the conservation properties and high accuracy of the proposed scheme. Finally the compact scheme is applied to study the convergence rate of the quantum Zakharov system to its limiting model in the semi-classical limit.

本文致力于开发和分析一种解决量子Zakharov系统的高精度保守方法。该方案基于线性隐式紧致有限差分离散化，并在离散级上节省了质量和能量。进行了详细的数值分析，表明该方法在空间上是四阶的，在时间上是二阶的。报告了几个数值示例，以确认所提出方案的保存特性和高精度。最后，将紧凑方案应用于研究量子Zakharov系统到其在半经典极限中的极限模型的收敛速度。