量子激发态最陡下降微扰理论

THE STEEPEST DESCENT PERTURBATION THEORY FOR THE EXCITED STATE OF A QUANTUM SYSTEM

本文发展了量子激发态能量与波函数的最陡下降微扰理论计算方法,该方法避免了普通微扰理论所需要的对于参考态的无限求和困难,并能通过逐步迭代计算逼近于体系精确的本征函数和本征值。只要保持激发态试探波函数正交于其对称性相同的低激发态或基态的波函数,避免计算过程中的变分坍陷,本文的方法能用于求精确的激发态能量和波函数。

The steepest descent perturbation theory is extended to the calculation of the energy and eigenfunction of the excited state of a quantum system. In case of the orthogonality of the trial function for the excited state to those for lower-energy state or ground state in the same symmetry class is preserved, the variational collapse to lower energy state can be avoided in this proposal. An iterative procedure is given for generating better eigenvalue and eigenfunction of the excited state without requiring an infinite summation over reference states as in conventional perturbation theory. This new perturbation method can be applied to calculate the excitation energy and wave function of excited states for any many-body quantum system to a high degree of accuracy without so much computational effort as in conventional method.