多项式势阱中粒子能级的微扰计算

Perturbation calculation of energy levels in a polynomial potential well

利用超位力定理(HVT)和Hellmann-Feynman定理(HFT),可把势阱中粒子能级的微扰计算简化为代数公式,从而方便计算机编程.对于可展开为多项式的势阱,综合考虑势能多项展开式中截断近似和有限级次的递推计算二者引入的误差,我们重新定义了近似计算的阶次.作为例子,我们给出了高斯势的能级近似计算.

Analysis of successive order approximation energy levels corresponding to successive orders of the perturbation terms in a power series expansion of the potential energy is processed with the use of hypervirial theorem (HVT) and Hellmann-Feynman theorem (HFT),and algebraic formulas for calculation are deduced.The results show that there are two related sources of computation errors involved:one is taking finite terms from the power series expansion for the potential energy,and the other is taking finite perturbation levels for the energy calculations,so a rational order is introduced to define the approximation levels.As a typical example,calculations up to the second order approximate eigenvalues for Gaussian potential profile are processed.