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.     

q类似玻色算符的逆算符及其应用

在q类似Fock空间中引入了q类似玻色算符的逆算利用的性质,构造了增光子相干态的q形变形式并讨论其完备性关系.     

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.     

Study on the orthonormalization eigenstates of α_q~3

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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.     

q-Deformed IWOP Technique and Its Applications

We extend the newly developed technique of integration with an ordered product (IWOP) of operators to q-deformed boson case. The ambiguity arising from defining the normal ordering of q-deformed boson operators, which satisfy aa^↑ - qa^↑a = 1, can be eliminated by following the q-deformed IWOP technique. Some new q-integration formulas and new qboson operator identities are obtained, and the P-representation of q-analogue of the chaotic state of radiation field is derived.     

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.     

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.     

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.     

Some q-Deformed Combinat orial Identities and Their Applications

A q-deformed binomial theorem is firstly presented in this work. Some operator identities in q-deformed two-mode Fock space are derived by virtue of the q-binomial theorem. As an application of these identities, we prove a new completeness relation for the q-analogue of the singlecomplex-variablestate in the two-mode Fock space.     

Deformation of the exterior algebra Ω(M n) and the Yang-Baxter equation

We show that the deformation of the exterior algebra on a given manifold is related to the existence of the Yang-Baxter equation. We prove that this deformed algebra involves a differential operator generating the algebra. The obtained differential calculus is not commutative and we recover the classical one for the classical limit of the deformation parameters. The q-analogue of the Leibniz rule corresponding to the purposed differential operator is given.     

D-Dimensional q-Harmonic Oscillator and d-Dimension q-Hydrogen Atom

A q-analogue of the D-dimensional harmonicoscillator is presented. A new realization of thequantum algebra SU_q(1,1) via theD-dimensional q-harmonic oscillator is found. A model ofthe d-dimensional q-hydrogen atom is constructed by means of theD-dimensional q-harmonic oscillator. The dimension D ofthe q-harmonic oscillator and the dimension d of theq-hydrogen atom are arbitrary.     

The Embedding of Quantum Algebra U(gl(n+1)) in Irreducible Representations of U(gl(n+1))

Using a formula derived by Jimbo, we express the generators of U(gl(n+1)), the q-analogue of U(gl(n+1)) in an irreducible representation with Gel'fand basis, as functions of the generators of U(gl(n+1)).     

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.     

INCOMPLETE q-GAMMA FUNCTION AND TRICOMI EXPANSION

In this paper, we introduce a q-analogue of the Tricomi expansion for the incomplete q-gamma function. A general method is described for converting a power series into an expansion in incomplete q-gamma function. Also, we use the q-Tricomi expansion for giving a formal proof of the relation between the incomplete gamma function and the exponential integral. Finally, we formally deduce the q-Tricomi expansion via the q-Taylor expansion.     

Boson Realization of Representations for Quantum Groups and Its Differential Correspondence in Bargmann Space

By constructing the q-analogue of the Heisenberg-Weyl algebra in terms of usual creation and annihilation operators of boson states in the Fock space, the boson realization method recently suggested^[7-11] is generalized to obtain a class of representations of quantum group in the Fock space. The q-deformed differential realization of quantum groups proposed by Alvarez-Gaume is derived by making use of the boson realization in this 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.     

On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes

A very well known result by Harish-Chandra claims that any Hermitiansymmetric space of non-compact type admits a canonical embedding into acomplex vector space V. The image of this embedding is a bounded symmetricdomain in V. This work provides a construction of q-analogues of apolynomial algebra on V and the differential algebra of exterior forms on V.A way of producing a q-analogue of the bounded function algebra in a boundedsymmetric domain is described. All the constructions are illustrated bydetailed calculations in the case of the simplest Hermitian symmetric spaceSU (1,1)/U(1).     

光子—声子相互作用模型的基态特性研究

采用新的相干态波函数的方法,对简单的光子－声子相互作用模型的基态特性进行了研究,非常简单地导出了模型的精确基态能与基态波函数,并且对其物理意义进行了讨论。     

压缩真空场与原子非线性作用系统中原子的量子特性

研究了附加克尔介质的压缩真空场与二能级原子依赖强度耦合相互作用系统中原子的反转特性,并采用密度算符间的距离研究了该模型中原子量子态的演化规律.详细地讨论了克尔非线性作用的强度以及初始压缩真空场的压缩度对原子反转和原子量子态演化的影响.