四次非谐振子激发态的高阶变分-积分微扰修正

Multi- Order Corrections of Variational- Integral Perturbation for Quartic Anharmonic Oscillator in the First Excited State

用改进变分-积分微扰法求解四次方非谐振子第一激发态.设置含有变分参数的母哈密顿量作为零级哈密顿量,选择该母哈密顿系统的精确解作为试探波函数,得到了只有几项的高阶修正波函数和高阶能量修正,与其它方法所得结果比较,该计算结果更接近精确能量值.结果表明,这种方法不仅可提高计算结果的精度,而且可改善微扰级数解的收敛性.

We apply the improved variational-integral perturbation method to solve the quartic anharmonic oscillator in the first excited state.Setting the female Hamiltonian including variational parameter as the zeroth-order Hamiltonian and choosing the exact solution of the female Hamiltonian system as the trial wave function,we obtain the multi-order corrected wave functions consisting of a few terms and calculate the multi-order energy corrections.Comparison with the results of other method,the former are quadratically integrable and the latter are in good agreements with the exact data.The boundedness and convergence of the perturbation series solution are also verified.The results show that the variational-integral perturbation method can not only raise precision of the result but also keep convergence of the perturbation series.