q变形算符α^N的本征态的结构及其高阶压缩性质

证明了高阶振幅压缩的概念可以应用于q变形代数的光场。q变形算符α^N的正交归一本征态的压缩特点由这些态的内部奇偶结构决定。破坏这种奇偶结构将得到具有新压缩特点的光场。     

几类粒子密度算符和粒子流密度算符的讨论

从粒子密度和粒子流密度出发,分析了几类相关的算符,讨论了它们的性质与相互关系;从具体的物理意义出发,明确了合适的粒子密度算符和粒子流密度算符的表达形式.     

一维Morse势动量算符矩阵元的通项公式

导出一维Morse势中动量算符矩阵元〈n|Ap^G2q|n′〉的通项计算公式.     

q变形算符aN的本征态的结构及其高阶压缩性质

证明了高阶振幅压缩的概念可以应用于q变形代数的光场。q变形算符aN 的正交归一本征态的压缩特点由这些态的内部奇偶结构决定。破坏这种奇偶结构将得到具有新压缩特点的光场。     

谐振子任意次幂动量算符矩阵元的计算

本文利用一维谐振子的升降算符合出了计算动量算任意次幂Ｐ＾ｋ的矩阵元及平均值通式，并建立了与坐标算符矩阵元的转换关系。     

双参数变形多模玻色算符的代数结构及其应用(Ⅰ)

构造了两个满足量子Heisenberg-Weyl代数的双参数变形多模玻色算符,研究了它们的代数结构,作为应用,给出了双参数变形多模量子群SU(2)_q,s和SU/(1,1)_q,s的Holstein-Primakoff实现,并分别构造了这两个玻色算符二次幂的本征态,证明了它们的完备性.     

q变形非简谐振子湮没算符高次幂本征态的反聚束特性

研究了q变形非简谐振子湮没算符高次幂本征态的反聚束特性,并用数值计算方法定量研究了变形参量q对这一特性的影响.结果表明,q变形非简谐振子湮没算符高次幂本征态在非谐振子强度x│=β│²的若干取值区间内可多次交替地呈现反聚束效应,并且变形参量q对这一效应有很大的影响.     

量子超代数splq(2,1)的q变形玻色-费米表示

本文分别运用一对q变形玻色算符、一对q变形费米算符与两对q变形玻色算符、两对q变形费米算符,给出了量子超代数spl_q(2,1)的两种q变形玻色-费米实现.     

对动量算符的讨论

既肯定Ｐ＝－ｉｈ△↓在任何坐标系中都是动量算符矢量,又否定它在曲线坐标系中的分量是动量分量的算符,作出这种判断不是出于主观认识,而是源于量子理论本身,分别在非相对论和相对论两种情形下导出了曲线坐标系中动量分量的算符,表明造成两者之间差别的原因是粒子的自旋。．     

The Entire Representation of q-Analogue Coherent,States

The en tire represen tation of q-analogue coherent states is established and the expansions for states and operators in this representation are given. Associated with this, a q-analogue of normal ordered operation is defined.     

Properties of the States Generated by the Excitations on a q-Coherent State

We study the mathematical and physical properties of the states which are generated by excitation on a q-analogue of the coherent state. With the help of a q-analogue of the Laguerre polynomial, the squeezing and the statistical properties of the field in such the state are also discussed.     

A Multi-Parameter Reduced Deformation of U(sl(r))

A multi-parameter reduced deformation of U(sl(m+n)) is constructed. This deformation has both the usual reduced q-analogue of U(sl(m+n)) and the reduced q-analogue of U(sl(m,n)) as its special quotients.     

Wigner Function and Phase Probability Distribution of q-Analogue of Squeezed One-Photon State

In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.     

A q-Analogue of Normal Ordered Operation

In this paper the operation of q-normal ordered product is realized in q-analogue bosonic oscillators. The expression of the vacuum projective operator in the form of q-operators is obtained, some initial applications about this operation are also given.     

Quantum Minkowski Space and the q-Analogue of Dirac Equation

The covariant differential calculus on the quantum Minkowski space is presented with the help of the generalized Wess-Zumino method and the quantum Pauli matrices. The quantum Dirac matrices are constructed parallel to those in the classical case. Combining these two aspects a q-analogue of Dirac equation follows directly.     

Study on the orthonormalization eigenstates of α_q~3

Ｓｔｕｄｙｏｎｔｈｅｏｒｔｈｏｎｏｒｍａｌｉｚａｔｉｏｎｅｉｇｅｎｓｔａｔｅｓｏｆα_ｑ~３￥ＸＩＡＤｅｙｏｎｇ（ＨａｒｂｉｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｈａｒｂｉｎ１５００８０，Ｃｈｉｎａ）ＲＥＮＭｉｎ，ＭＡＡｉｑｕｎ（ＨａｒｂｉｎＣｏｌｌｅｇ...     

q-Analogue Charged Coherent State and SU(3) Charged,Hypercharged Coherent State

We generahe the conception of q-analogue coherent state to the cases of charged coherent state and charged, hypercharged coherent state. Their explicit expressions in the ordinary Fock space are derived.     

Tauberian Theorems In Quantum Calculus

Abstract

In this paper we attempt to establish some tauberian theorems in quantum calculus. This constitutes the beginning of the study of the q-analogue of analytic theory of numbers which is the aim of a forthcoming paper.     

q-Laguerre Polynomial Realization of gl√q(N)-Covariant Oscillator Algebra

It is shown that the q-analogue of the groupelement of gl_q-(N)-covariant oscillatoralgebra can be written in terms of the q-deformedLaguerre polynomials.