CAJ | 학술논문

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.
용개진변분-적분미우법구해사차방비해진자제일격발태.설치함유변분삼수적모합밀돈량작위령급합밀돈량,선택해모합밀돈계통적정학해작위시탐파함수,득도료지유궤항적고계수정파함수화고계능량수정,여기타방법소득결과비교,해계산결과경접근정학능량치.결과표명,저충방법불부가제고계산결과적정도,이차가개선미우급수해적수렴성.
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.