The highly excited vibrational states of quasi-linear tetraatomic molecule HCNO are studied in the framework of U(4) algebra. By using symmetric group with which the tetraatomic molecules satisfy, we construct the alg...The highly excited vibrational states of quasi-linear tetraatomic molecule HCNO are studied in the framework of U(4) algebra. By using symmetric group with which the tetraatomic molecules satisfy, we construct the algebraic Hamiltonian that not only includes Majorana operator M 12 but also M 13 and M 23 which are very useful for getting potential energy surface and force constants in Lie algebra method. And the eigenvalue of the Hamiltonian are obtained by Lie algebra treatment.展开更多
在前面的纸[Commun。Theor。Phys。 51 ( 2009 ) 321 ]我们为解开在 exp 形式的指数的操作员推荐了一个方便方法{B + C }，试着发现操作员 A 那满足[一， B ]= C ，并且[一，[一， B ]]= 0 ，然后，从面包师 Hausdorff 公式，我们有 exp...在前面的纸[Commun。Theor。Phys。 51 ( 2009 ) 321 ]我们为解开在 exp 形式的指数的操作员推荐了一个方便方法{B + C }，试着发现操作员 A 那满足[一， B ]= C ，并且[一，[一， B ]]= 0 ，然后，从面包师 Hausdorff 公式，我们有 exp {B + C }= exp {B+[一， B ]}= e <SUP ></SUP> e <SUP > B </SUP> e <SUP>−A</SUP>。在安排 e <SUP 以后 ></SUP> e <SUP > B </SUP>= e <SUP > B </SUP> e <SUP ></SUP> e <SUP > W </SUP>, 解开的 exp {B + C }= e <SUP > B </SUP> e <SUP > W </SUP> 被获得。特别，在这个工作，我们使用这个方法到二模式的大小写导出 exp 的正常征订表[h (<SUP>†</SUP >+ b <SUP>†</SUP > b )+ ga <SUP>†</SUP > b <SUP>†</SUP>+ kab ] 没有呼吁谎言代数学方法。展开更多
The integrated gradient of a quadrupole will be deviated by a close neighboring sextupole, and this is called the effect of fringe field interference. Using the Lie algebra techniques, an analytical expression for the...The integrated gradient of a quadrupole will be deviated by a close neighboring sextupole, and this is called the effect of fringe field interference. Using the Lie algebra techniques, an analytical expression for the betatron tune shift due to this effect has been derived. The process does not depend on the supposition of the thin-lens quadrupoles. It can be used to estimate the tune shift differences between the designed lattice and the one including the fringe field interference. More generally, the method can be applied to other kinds of fringe field interference.展开更多
O431 97020711强激光场中双原子分子多光子激发的李代数方法=Lie algebraic approach to the multiphoton ex-citation of vibrational states of diatomicmolecules in intense laser fields[刊,中]/袁峰,丁世良(山东大学理论化学研究...O431 97020711强激光场中双原子分子多光子激发的李代数方法=Lie algebraic approach to the multiphoton ex-citation of vibrational states of diatomicmolecules in intense laser fields[刊,中]/袁峰,丁世良(山东大学理论化学研究室.山东,济南(250100))//物理学报.-1996,45(1).展开更多
文摘The highly excited vibrational states of quasi-linear tetraatomic molecule HCNO are studied in the framework of U(4) algebra. By using symmetric group with which the tetraatomic molecules satisfy, we construct the algebraic Hamiltonian that not only includes Majorana operator M 12 but also M 13 and M 23 which are very useful for getting potential energy surface and force constants in Lie algebra method. And the eigenvalue of the Hamiltonian are obtained by Lie algebra treatment.
基金supported by the National Natural Science Foundation of China under Grant Nos.10775097 and 10874174
文摘在前面的纸[Commun。Theor。Phys。 51 ( 2009 ) 321 ]我们为解开在 exp 形式的指数的操作员推荐了一个方便方法{B + C }，试着发现操作员 A 那满足[一， B ]= C ，并且[一，[一， B ]]= 0 ，然后，从面包师 Hausdorff 公式，我们有 exp {B + C }= exp {B+[一， B ]}= e <SUP ></SUP> e <SUP > B </SUP> e <SUP>−A</SUP>。在安排 e <SUP 以后 ></SUP> e <SUP > B </SUP>= e <SUP > B </SUP> e <SUP ></SUP> e <SUP > W </SUP>, 解开的 exp {B + C }= e <SUP > B </SUP> e <SUP > W </SUP> 被获得。特别，在这个工作，我们使用这个方法到二模式的大小写导出 exp 的正常征订表[h (<SUP>†</SUP >+ b <SUP>†</SUP > b )+ ga <SUP>†</SUP > b <SUP>†</SUP>+ kab ] 没有呼吁谎言代数学方法。
基金Supported by the National Science Foundation of China under Grant No. 20173013Partial Financial Supports from the Science Foundation of Shandong Province under Grant No. Y2008C102the Foundation of Taishan Meidical College under Grant No. TSB016
基金support and assistance. This work was supported by National Natural Science Foundation of China (No. 11105165)
文摘The integrated gradient of a quadrupole will be deviated by a close neighboring sextupole, and this is called the effect of fringe field interference. Using the Lie algebra techniques, an analytical expression for the betatron tune shift due to this effect has been derived. The process does not depend on the supposition of the thin-lens quadrupoles. It can be used to estimate the tune shift differences between the designed lattice and the one including the fringe field interference. More generally, the method can be applied to other kinds of fringe field interference.
基金Supported by the National Natural Science Foundation of China under Grant No 10775092, Shanghai Leading Academic Discipline Project under Grant No S30105, and the Training Fund of NENU＇S Scientific Innovation Project under Grant No NENU-STC08018.
文摘我们主要基于谎言代数学的方法探索忠实危险性。在物理根据上，忠实危险性罐头的准确表情分别地在苏(2 ) 和代数学的结构建模的苏(1,1 ) 被获得，它被用于一个身体系统和许多身体系统，例如单个旋转模型，单个模式挤压泛音振荡器模型和英国计算机学会模型。以快步行走绿色功能的方法，我们的一般结论与在有限温度和 T = 展出忠实危险性的二个模型一起被说明 0。[从作者抽象]
文摘O431 97020711强激光场中双原子分子多光子激发的李代数方法=Lie algebraic approach to the multiphoton ex-citation of vibrational states of diatomicmolecules in intense laser fields[刊,中]/袁峰,丁世良(山东大学理论化学研究室.山东,济南(250100))//物理学报.-1996,45(1).
