Multigrid methods for linear equations diagonalized by gft 对角化系统的多重网格方法
2.
Then the hamiltonian of the io algebraic model was diagonalized on the symmetrical bases , and the energy spectra of benzene and the corresponding wave function are obtained 在对称基上将io代数模型中的哈密顿量对角化，得到苯分子振子数高达10的能谱及相应的波函数。
3.
Zijingguan fault zone is the main structure in taihang mountains that are located in the central part of 20 ~ 30 ne - striking daxing ' anling - taihan - wuling tectonic belt . it is composed of two diagonalized faults that are wulonggou - shanghuangqi fault located in the west and zijingguan - lishan fault in the east 紫荆关断裂带是大兴安岭?太行山?武陵山构造带中段太行山地区的主体构造，总体走向20 30 ，由西侧的乌龙沟?上黄旗断裂和东侧的紫荆关?灵山断裂左阶斜列组成。
4.
We examin e the generation of bell state in bose - einstein condensates of two interacting species trapped in a double - well configuration analytically and the density of probability for finding the entangled bell state is given . we find that the oscillation amplitude of the probability of density for finding the entangled bell state becomes greater as the ratio of the interspecies interaction strength and the tunneling rate increases , moreover the self - interaction strength of the component a ( b ) has no effect on it . also we use the time - dependent su ( 2 ) gauge transformation to diagonalize the hamilton operator , obtain the berry phase and analytically the time - evolution operator 此外我们还研究了在双阱玻色-爱因斯坦凝聚中纠缠态的演化，研究发现随着组分间相互作用和随穿率的比值的增加系统演化到bell态的概率变大，而且组分自身内在的相互作用对形成bell态的几率没有影响；并且用含时su ( 2 )规范变换对角化哈密顿量得到了系统的berry位相和时间演化算符，并研究了量子随穿过程。
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Expanding the system ' s hamiltonian to a real symmetric matrix in an appropriate orthogonal basis vector and then diagonalizing it , we get the energy spectrum of the system and calculate the energy level spacing distribution function and the spectral rigidity . then we study the statistical character of the energy spectrum under the changing of magnetic field intension and find that the system ' s motion transfers from regular to chaos gradually 将系统的哈密顿量在一个适当的正交基矢下展开并对角化，得到系统的能谱，分别计算系统能谱的能级间距分布函数和谱刚度，研究了该系统量子能谱的统计特征随磁感应强度大小的改变而表现出的系统运动由规则到混沌的渐进变化。
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By using the new method , the eigenstate of xxz antiferromagnetic model is solved , which is revealed to be 5 ? l , l ) coherent state . in the third chapter , we discussed the relation between the bogoliubov - valatin transformation and the algebraic method based upon the bcs model hamiltonian at first . then , we diagonalized the ssh model hamiltonian for the first time by using the algebraic diagonalization method 第三章我们首先使用bogoliubov - valatin变换对角化和新的代数对角化两种方法，将bcs模型的哈密顿量对角化，并对两种对角化方法作了比较、讨论；其后，本文首次给出了代数对角化方法在ssh模型中的应用，并且其结果也与bv变换法的作了同上面bcs模型类似的讨论。
