四次非谐振子的高阶变分-积分微扰修正  

Multi-Order Corrections of Variational-integral Perturbation for Quartic Anharmonic Oscillator

作　　者：赵云辉[1] 海文华[1] 申莉华[2] 

机构地区：[1]湖南师范大学物理与信息科学学院,中国长沙410081 [2]邵阳学院理学与信息科学系,中国邵阳422000

出　　处：《湖南师范大学自然科学学报》2008年第3期50-55,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(10575034);湖南省教育厅科学与技术研究基金资助项目(07C682)

摘　　要：利用基于积分方程的改进的变分微扰方法(变分-积分微扰法)求解四次方非谐振子基态.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,与其他方法所得结果比较,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.The improved variational-perturbation method based on integral equation （variational-integral perturbation method） is applied to solve the quartic anharmonic oscillator in the ground 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 convereence of the nerturbation series.

关 键 词：非谐振子 变分-积分微扰法 高阶能量修正 

分 类 号：O413.1[理学—理论物理]