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1.
利用二次型理论构造一个幺正矩阵进行表象变换,将|x〉表象中的三模坐标-动量耦合量子谐振子体系的哈密顿量对角化,这不仅提供了一种解决该类问题的一般数学方法,同时对培养和提升学生运用数学工具解决复杂物理问题的能力也具有积极的指导作用. 相似文献
2.
本文用不变本征算符方法研究非对易相空间中三模坐标动量耦合谐振子的能谱,分别得到了非耦合和坐标动量耦合两种情况下谐振子能谱的解析解,其中包括受非对易参数θ和φ影响的解λ0,1和λ1,1,以及不受非对易参数θ和φ影响的解λ0,2和λ1,2.然后,分析了两类耦合参数κ和η对三模坐标动量耦合谐振子能谱的影响.结果发现,耦合参数κ和η对λ1,1的影响是相同的,且当κ=η时,耦合系数κ和η对λ1,1是没有影响的. 相似文献
3.
New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application 下载免费PDF全文
We construct four linear composite operators for a two-particle
system and give common eigenvectors of those operators. The
technique of integration within an ordered product (IWOP) of
operators is employed to prove that those common eigenvectors are
complete and orthonormal. Therefore, a new two-mode intermediate
momentum-coordinate representation which involves quantum
entanglement for a two-particle system is proposed and applied to
some two-body dynamic problems. Moreover, the pure-state density
matrix | ξ 1 ,ξ 2 >C,DC,D< ξ 1 ,ξ 2 | is a Radon
transform of Wigner operator. 相似文献
4.
New Approach for Calculating Tomograms of Quantum States by Virtue of the IWOP Technique 总被引:1,自引:0,他引:1
FAN Hong-Yi WANG Ji-Suo 《理论物理通讯》2007,47(3):431-436
We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ) and [x,μ, ν) (named the intermediate coordinate-momentum representation), and the two Radon transforms of the Wigner operator are just the pure-state density matrices [p)σ1τσ1τ (p| and (p)λ,ν,λ,ν,(x| respectively. As a result, the tomogram of quantum states can be considered as the module-square of the states' wave function in these two representations. Throughout the paper we fully employ the technique of integration within an ordered product of operators. In this way we establish a new convenient formalism of quantum tomogram. 相似文献
5.
XU Shi-Min XU Xing-Lei LI Hong-Qi WANG Ji-Suo 《理论物理通讯》2009,51(2):209-214
We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new intermediate coordinate-momentum representation for a two-particle system is proposed and applied to some two-body dynamic problems. 相似文献
6.
荆雪蕾 《原子与分子物理学报》2010,27(2):293-297
利用退激发压缩真空态归一化函数的产生函数, 获得了归一化的退激发压缩真空态. 借助于此态的归一化常数和中介表象理论, 我们得到了退激发压缩真空态的量子Tomogram函数和一些新的数学公式. 相似文献
7.
FAN Hong-Yi LOU Sen-Yue 《理论物理通讯》2008,49(3):613-616
We introduce bivariate normal distribution operator for state vector [ψ) and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability |λ,v〈x|.ψ〉|^2, where |x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function. 相似文献
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Normal ordering and antinormal ordering of the operator (fQ+gP)n and some of their applications 下载免费PDF全文
In this paper by virtue of the technique of integration within an ordered product (IWOP) of operators and the intermediate coordinate-momentum representation in quantum optics, we derive the normal ordering and antinormal ordering products of the operator (f Q + gP )n when n is an arbitrary integer. These products are very useful in calculating their matrix elements and expectation values and obtaining some useful mathematical formulae. Finally, the applications of some new identities are given. 相似文献
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11.
Optical scaled Fresnel--Fourier transform obtained via intermediate coordinate-- momentum representation 下载免费PDF全文
Using the intermediate coordinate--momentum representation
|x>s,r, we introduce a new Hadamard
transform. It is found that the operator U corresponding to this
transform can be considered as a combination of the Fresnel operator
F(r,s) and the Fourier transform operator F
by decomposing U. We also find that the matrix element
s,r< x| U|f>
just corresponds to an optical scaled Fresnel--Fourier transform. 相似文献
12.
FAN Hong-Yi TANG Xu-Bing 《理论物理通讯》2008,49(5):1169-1172
Using the technique of integration within an ordered product (IWOP) of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation that is an operator generalization of the solution of thermo conduction equation. Then we seach for the solution of operator Fredholm integration equations, which provides us with a new approach for deriving some operator identities. 相似文献
13.
借助在Majorana表象下提出的纠缠度定义, 研究了对称双阱中两个玻色原子组成的系统的纠缠动力学. 得到了系统的任意态在Majorana 表象下的表示, 并考察了原子间相互作用及系统初始状态对纠缠度动力学的影响. 发现原子间相互作用会决定纠缠度振荡的频率, 而纠缠度振荡的幅度对系统的初态很敏感. 相似文献
14.
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 functions for the photon-depleted even and odd coherent states (PDEOCSs). Moreover, in terms of the Wigner functions with respect to the complex parameter a the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state |β, m〉o (or |β,m〉e) is more pronounced when m is even (or odd). According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics. 相似文献
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Based on the rotation transformation in phase space and
the technique of integration within an ordered product of operators,
the coherent state representation of the multimode phase shifting
operator and one of its new applications in quantum mechanics are
given. It is proved that the coherent state is a natural language
for describing the phase shifting operator or multimode phase
shifting operator. The multimode phase shifting operator is also
a useful tool to solve the dynamic problems of the multimode
coordinate--momentum coupled harmonic oscillators. The exact energy
spectra and eigenstates of such multimode coupled harmonic
oscillators can be easily obtained by using the multimode phase
shifting operator. 相似文献
18.
We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well. 相似文献
19.
We derive properties of N-extended
super Virasoro algebras. These include adding central extensions, identification of all primary fields and the action of the adjoint representation on its dual. The final result suggest identification with the spectrum of fields in supergravity theories and superstring/M-theory constructed from NSR N-extended supersymmetric
Virasoro algebras. 相似文献
20.
PANG Qian-Jun 《理论物理通讯》2005,44(9)
We study the eigenstate problem of a kind of coupled oscillators in the new quantum mechanical represen tation |q, μ, v〉, which is defined as the eigenvector of the operator (μQ vP), where μ and v are two realparameters. We also use the U operator transformation method to deal with the same problem. We obtain the normally ordered product expressions of U operator and eigenvector. It is shown that the ground state of system Hamiltonian is a squeezed state. 相似文献