Abstract : the wavefunctions and energy eigenvalues for the ring - shaped oscillator are obtained using the ideas of supersymmetric quantum mechanics and shape invaricace 文摘:采用量子力学中的超对称性和形不变性，讨论环形振子的波函数和能量本征值
This method is easy in controlling mse by choosing the number of reservation eigen values . in the end , the pca algorithm based on neural network is proposed 该方法主要的优点是可以通过控制选取保留的本征值个数来调整误差，使得舍入误差控制在要求的范围内。
Alpha eigenvalue is an characteristic parameter in neutron chain reaction physics . it describes the variational velocity of neutron flux along with time 本征值是中子链式反应物理中表征系统动态性质的一个重要特征量，描述中子通量密度随时间按指数规律变化的快慢。
Aim at the above problem , this article obtained following creative results : 1 . base on the keno - iv code , - keff iteration model has been constructed in this thesis 在蒙特卡罗程序keno -的基础上，建立了- k _ ( eff )迭代计算模型，从原理和方法上解决了本征值问题的计算。
Therefore , we have constructed the calculations model of - eignevalue problem , and on the basis of keno code , developed the mc code of - eigenvalue problem 为此，我们从对本征值问题计算模型的研究出发，在原有keno程序的基础上，研制出了计算本征值问题的蒙特卡罗程序。
By omitting certain particular conditions inconsistent with actualities , we can also obtain a similar result in the position distribution of discrete eigenvalues and their limit points for this kind of operators 在省略某些不符合实际的特殊条件的情况下，对这类算子离散本征值及其聚点的位置分布，同样获得了一个类似的结果。
However , the exact eigenvalues can be obtained only for simple geometries , like as rectangular and cylindrical resonator . for arbitrarily shaped cavities and dielectric - loaded cavities . numerical techniques must be used 但是,实际中仅仅对于一些简单几何形状的谐振腔可以得到准确的本征值和场分布,比如矩形谐振腔、圆柱谐振腔等。
The nuclear fissile reaction system , which provides nuclear energy or neutrons , theoretically demands its criticality safety and neutron energy spectrum to be predicated . generally , those are realized by calculating the k - eigenvalue problem 对于提供核能源或中子源的核裂变反应系统，需从理论上给出它的临界安全性和中子能谱，通常通过k本征值问题的计算来实现。
By this model , the - eigenvalue problem can be treated as a series of k eigenvalue problems with a certain number which is adjusted by keff . the monte carlo code for calculating eigenvalue problem has been developed in this thesis 该模型把本征值问题的计算转化成带参数的一系列k本征值问题的计算，其参数值的调节通过上一次迭代计算的k _ ( eff )来实现。
This code has been used to calculate the - eigenvalue problem and the calculation results of - eigenvalue , correspond spectra and correspond reaction rates are consistent with the predication of the theory , and gained the practical results 计算所得入本征值、入本征值能谱与理论预言吻合。为反应堆等核裂变系统的核临界安全分析和中子核反应率的计算提供了有意义的结果。
