基于线性变分法，提出了一种计算任意阶多项式势场中粒子能量本征值的简单方案，通过选取带参数的谐振子本 征函数为基函数，并结合坐标任意次幂的谐振子矩阵元计算通式，推导出体系哈密顿矩阵元的代数表达式，并根据哈密顿矩 阵的迹相对谐振子本征函数的参数取极小确定该参数值.

We present a simple scheme to calculate the energy eigenvalues of particle bounded in the polynomial potential by using the linear variational method. The wave functions of the harmonic oscillator (HO)including one parameter are chosen as the basis functions，and the general formula of the Hamiltonian matrix element (HME) of coordinate operator for the HO is utilized. The algebraic expression of the system’s HME is derived. The HO parameter is determined from the rule that the trace of the Hamiltonian matrix takes the minimum value relative to this parameter.