激发态的最速逼近微扰理论

本文将文献［１］提出的应用于量子体系基态的最速逼近微扰理论（ＳＡＰＴ）推广到了激发态。本文证明，只要保持激发态尝试波函数正交于对称性相同的激发态或基态波函数，就能避免计算过程的变分坍陷，并通过逐步迭代（逐一计入其他各态的贡献）计算逼近体系精确的激发态能量和相应的波函数，且不存在瑞利－薛定谔微扰理论（ＲＳＰＴ）的无穷求和和最陡下降微扰理论（ＳＤＰＴ）需计算哈密顿量二次和三次方矩阵元的困难。本文的方法可用于求精确的激发态能量和波函数。

THE STEEPEST APPROXIMATION PERTURBATION THEORY OF THE EXCITED STATE

In this paper, the steepest approximation perturbation theory[1]for the ground state of a quantum system is extended to excited states. In case the orthogonality of the trial function for the excited state to that for lower-energy state or ground state in thd same symmetry class is preserved, the variational collapse to lower energy state can be avoided in this proposal. The accuracy is raised by reckoning in contribution of other states step by step. but the difficulties that Reyleing-Schrodinger perturbation theory (RSPT) must be summed up infinitely and that steepest descent perturbation theory (SDPT) has to calculate Hamiltonian's square and cubic matrix elements are avoided in this method. This new perturbation method can be applied to;calculate the exact energy eigenvalve and wave function of excited state of a quantum system.