粒子数态波函数推导的新方法

Fock表象是量子光学理论中的基本表象,我们给出粒子数态｜n＞在坐标表象＜x ｜中的波函数的新方法,我们用有序算符内积分技术(IWOP)推导它,这一形式具有简洁优美的特点,并且可推广到其它情形.例如可以探讨在引入双模纠缠态表象后,双模粒子数态的波函数.     

基于算符正规乘积的若干厄米多项式关系式证明

主要利用量子力学的方法证明了厄米多项式的递推关系.另外,根据厄米多项式的表达式,得出了两个与厄米多项式有关的积分公式.     

厄米多项式算符的新恒等式及其在量子压缩中的应用

通过发现有关厄米多项式算符H_n(X)的恒等式, 并结合有序算符内的积分技术, 得到了一些关于量子压缩的算符新恒等式, 这对于研究压缩粒子数态波函数十分有用.     

量子光学理论中双模厄米多项式的新应用

强调双模厄米多项式在量子光学理论中的地位,认为它是研究连续变量纠缠态和压缩态的必要函数,具有明确的物理意义。利用双模厄米多项式,结合有序算符内的积分技术,给出了若干新的算符恒等式和互逆的积分变换公式,证明了压缩双模粒子数态恰好是双变量厄米多项式激发压缩真空态。     

以双变量厄米多项式表达的量子光学基本恒等式

在量子光学理论计算中,经常遇到算符的正规排序和反正规排序问题,我们从双变量厄米多项式H_m,n(x,y)的母函数出发,导出两个简洁的重要的基本算符恒等式并由此可以给出一些推论公式。     

厄米多项式的定义及其他

分析了关于厄米多项式的争论.介绍了厄米多项式的两种定义.     

也谈厄米多项式的递推关系

由厄米多项式的母函数出发,推导出厄米多项式的递推关系以及厄米多项式中系数的递推关系.     

用压缩态理论导出偶-奇数阶厄密多项式的无穷和

利用有序算符内积分技术,用压缩态理论导出偶数阶厄密多项式H2n(x)和奇数阶H2n+1(x)的无穷和。并提出用量子力学算符Hermite多项式方法计算奇-偶相干态的波函数。我们用的新途径具有物理意义鲜明的特点。     

正规和反正规排列互换算符公式的推导

用文献[1]中提出的有序算符内的积分技术,简洁地导出了[量子光学学报,2002,8(1):8-12]一文中给出的有用的光场算符公式,并引入了双模厄米特多项式来表达这些公式.     

谐振子系统坐标算符矩阵元的简单计算方法

详细讨论了在粒子数表象和相干态表象中如何简捷地计算谐振子系统坐标算符矩阵元的问题,给出了具体的计算过程并对文献中的相关处理方法和过程进行了评述.     

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.     

Nonclassicality of a two-variable Hermite polynomial state

The nonclassicality of the two-variable Hermite polynomial state is investigated. It is found that the two-variable Hermite polynomial state can be considered as a two-mode photon subtracted squeezed vacuum state. A compact expression for the Wigner function is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the Wigner function. Then violations of Bell’s inequality for the two-variable Hermite polynomial state are studied.     

Wigner function and tomogram of the Hermite polynomial state

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner function for the Hermite polynomial state (HPS). The tomogram of the HPS is calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.     

Normal Ordering Expansion of Hermite Polynomials of Radial Coordinate Operator in Three-Dimensional Coordinate Space

For Hermite polynomials of radial coordinate operator in three-dimensional coordinate space we derive its normal ordering expansion, which are new operator identities. This is done by virtue of the technique of integration within an ordered product of operators. Application of the new formulas is briefly discussed.     

New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two-Variable Hermite Polynomials

Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators‘ ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials H and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such asa man =:Hm,n(a ,a):, ana m = (-i)m n:Hm,n(ia ,ia): are obtained.     

New optical field operator expansion in number state representation

By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields’(coherent state,squeezed field,Wigner operator,etc.) new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

A new type of photon-added squeezed coherent state and its statistical properties

We construct a new type of photon-added squeezed coherent state generated by repeatedly operating the bosonic creation operator on a new type of squeezed coherent state [Fan H Y and Xiao M 1996 Phys. Lett. A 220 81]. We find that its normalization factor is related to single-variable Hermite polynomials. Furthermore, we investigate its statistical properties, such as Mandel’s Q parameter, photon-number distribution, and Wigner function. The nonclassicality is displayed in terms of the intense oscillation of photon-number distribution and the negativity of the Wigner function.     

Two-Variable Hermite Polynomial Excitation of Two-Mode Squeezed Vacuum State as Squeezed Two-Mode Number State

We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state （THPES）. We find that the Wigner function of THPES and its marginal distributions are just related to two-variable Hermite polynomials （or Laguerre polynomials） and that the tomogram of THPES can be expressed by one-mode Hermite polynomial.