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1.
正规排列和反正规排列相互展开的计算 总被引:1,自引:1,他引:0
文章给出了产生算符和湮灭算例的正规排列与反正规排列相互展开的二个计算公式为(^a)^n(^a^ )^m=p/∑/k=0m!n!/(m-k)!(n-k)!k!(^a^ )^m-k(^a)^n-k和(^a^ )^n(^a)^m)=p/∑k=0(-1)^km!n!/(m-k)!(n-k)!k!(^a)^m-k(^a^ )^n-k,式中求和的上项p取m和n中较小的一个正整数。并用数学归纳法进行了证明,本文给出的这二次公式可广泛应用于各类激发态光场量子统计性质的研究。 相似文献
2.
采用新的方法,推导出三维各向同性谐振子径向基本算符r,r,1r对本征函数的作用结果,由此得出其升降算符及其他新的公式,并证明文献[1]中的结论有误
关键词:
基本算符 升降算符 三维谐振子 相似文献
3.
EPR型连续变量纠缠态的正规乘积方法求解 总被引:1,自引:1,他引:0
提出了一种求解EPR型连续变量纠缠态在Fock表象中的具体形式的方法.该方法利用量子场论中的正规乘积的性质,通过对正规乘积形式的玻色子算符函数的运算,导出了Fock表象中两粒子EPR型连续变量纠缠态(即两粒子算符X1-X2和P1 P2的共同本征态)的具体形式.该方法可以进一步推广至多粒子EPR型纠缠态相应具体形式的求解.因而,这是一种求解此类纠缠态在Fock表象中具体形式的普遍技术. 相似文献
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5.
本文引进了sd玻色子的6维无迹算符。按照类似于文献[1,2]中的方法,首先用这些算符构成SU_6?SO_6?SO_5?SO_3波函数,然后求出用通常的s~ d~ 算符表达的明显公式。 相似文献
6.
通过指数算符的分解,给出了SU(1,1)李代数玻色指数算符的正规和反正规乘积. 相似文献
7.
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Hm,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。 相似文献
8.
Wigner算符的正规乘积形式和相干态形式的应用 总被引:1,自引:0,他引:1
本文导出了Wigner算符的正规乘积形式和相干态形式及其若干应用, 其中包括若干新量子算符公式的导出, Moyal定理的相干态推广, 计算以前文献未曾得到的若干与经典函数对应的量子Weyl算符以及若干与量子算符对应的Weyl经典函数. 相似文献
9.
角动量阶梯算符在量子力学中有着极其广泛的应用,传统的教科书只给出角动量磁量子数的阶梯算符本文介绍一个新的总角动量阶梯算符,它可使总角动量量子数j上升(或下降). 在量子力学中,力学量用厄米算符表示,力学量之间的内在联系体现在对易关系中.因此,在一些问题中,不需解薛定谔方程,便可确定本征值及本征矢.其办法是构造出一个阶梯算符,例如对谐振子[1]、角动量[2]的处理.特别在处理角动量问题时,引入了阶梯算符L+(J+),由此推导出角动量的本征值、本征矢及有关矩阵元公式等. 那么,是否可以找出关于总角动量量子数的阶梯算符呢?目前的教科… 相似文献
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11.
SHAO Yu-Chong FAN Hong-Yi 《理论物理通讯》2008,49(4):866-870
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. 相似文献
12.
FANHong-Yi 《理论物理通讯》2002,38(6):729-732
In the context of the nonlinear coherent state(NLCS)theory we introduce the generalized weyl ordering operator formulation.The corresponding generalzied wigner operator turns out to be the Weyl ordered diracδ-operator functions.The completeness relation of NLCS is recast into generalized Weyl ordering form,The relationship between normal ordering,antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS. 相似文献
13.
FAN Hong-Yi 《理论物理通讯》2002,38(12)
In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl orderingoperator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operatorfunctions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship betweennormal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistenttheory for NLCS. 相似文献
14.
FAN Hong-Yi 《理论物理通讯》2008,50(5):1089-1092
We re-explain the Weyl quantization scheme by virtue of the technique of
integration within Weyl ordered product of operators, i.e., the Weyl
correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave. 相似文献
15.
P. Blasiak A. Horzela K.A. Penson A.I. Solomon 《Czechoslovak Journal of Physics》2004,54(11):1179-1184
We solve the normal ordering problem for (A
A)
n
where A and A
are one mode deformed ([A,A
] = [N+1] – [N]) bosonic ladder operators. The solution generalizes results known for canonical bosons. It involves combinatorial polynomials in the number operator N for which the generating function and explicit expressions are found. Simple deformations provide examples of the method. 相似文献
16.
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. 相似文献
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18.
FAN Hong-Yi 《理论物理通讯》2003,40(10)
By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for derivingmiscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can alsobe easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transformsand the squeezing transforms in quantum optics is investigated. 相似文献
19.
In this paper, we provide a simple and neat approach to some operators’ normal ordering and antinormal ordering formulas in
quantum optics. Namely, we directly adopt the generating function of Hermite polynomial and the Baker-Hausdorff formula, which
differs from the existing ways. As an important byproduct, based on these operator identities, some useful mathematical integral
formulas are easily given without really performing these integrations. 相似文献
20.
FANHong-Yi 《理论物理通讯》2003,40(4):409-414
By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated. 相似文献