Operator method and eigenvalues of the triple-well anharmonic oscillator

Using an algebraic technique based on the Lie algebra of the group SO(2, 1) the eigenvalues of the triple-well anharmonic oscillator are calculated for all ranges of the coupling constant. Approximate analytic formulas for the eigenvalues up to second order are given. The results obtained are compared with those of other authors.     

三级近似束流光学计算程序

为了精确计算束流在离子光学系统中的传输,用Visual FORTRAN 6.5语言编写了一个计算程序,长约13000行. 此程序可以计算由三圆筒单透镜、三膜片单透镜、双元筒透镜、均匀场静电加速管、磁四极透镜、六极磁铁、静电四极透镜、偏转磁铁、螺线管透镜、ExB~正交电磁场分析器、静电偏转器、漂浮管、QWR(Quarter Wave Resonators)和SLR(Split Loop Resonators)射频加速元件等元件任意组成的离子光学系统. 粒子轨迹的计算可精确到三级近似. 粒子的分布类型也可以有多种选择. 程序具有最优化计算功能,即可以自动调整元件的参数,以实现所需要的光学条件. 各元件之后的横向和纵向相图以及系统的束流包络线以图形方式显示在屏幕上.     

Quantum World with Quantum Time

Since the beginning of quantum mechanics there have been a lot of attempts to quantize time. In this paper we refer to the little known concept of quantum time proposed by E.Kapuscik [Hadronic J. 8 (1985) 75]. We analyze some properties of systems with quantum time. Moreover we comment and discuss the idea of quantum time.     

A New Loop Algebra and Its Corresponding Multi-component Integrable Hierarchy

A type of new loop algebra $\tilde{G}_M$ is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.     

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi-component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.     

Matrix Lie Algebras and Integrable Couplings

Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.     

Aspects of Pre-quantum Description of Deformed Theories

We discuss deformations of the classical systems in the phase space and show that one can use non-canonical transformations to relate regular and deformed models. On the other hand some of the models can be obtained as a classical limit of the deformed quantum models, i.e. as the result of the dequantization procedure. Nonrelativistic deformations are described.     

A New Quantum Analog of the Brauer Algebra

We introduce a new algebra depending on two nonzero complex parameters z and q such that its specialization at z=q ⁿ and q=1 coincides the Brauer algebra. We show that the action of the new algebra commutes with the representation of the twisted deformation of the enveloping algebra U(o _n) in the tensor power of the vector representation.     

A diagrammatic categorification of the fermion algebra

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional （1D） fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exnetlv with those in normal quantum mechanics.