共查询到19条相似文献,搜索用时 218 毫秒
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借助粒子数算符的本征矢及其完备性,得到了用实数x、产生算符及粒子基态表示的矢量|x〉.以此为起点,证明了矢量|x〉是坐标算符的本征矢,坐标投影算符的积分是单位算符,坐标本征矢是正交归一的.因此,坐标本征矢集{|x〉}具有正交归一性和完备性. 相似文献
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借助湮没算符的本征值方程及其本征态的完备性,证明了纠缠态的完备性.在此基础上,利用纠缠态所满足的本征值方程,得到了非对称纠缠态投影算符的积分.
关键词:
完备性
纠缠态
投影算符
积分 相似文献
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利用有序算符正规乘积内的积分技术(IWOP)和待定系数法,推导出了两粒子相对坐标算符x^1-x^2与总动量算符p^1 p^2的共同本征矢|η〉在Fock空间中的展开式,为解决这类问题提供了一种行之有效的方法,这对提高学生的学习素质和加深学生对理论知识的理解会有一定的帮助. 相似文献
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谐振子是量子力学中最基本也是十分典型和重要的问题,而在坐标表象中利用薛定谔方程的求解过程比较复杂.本文从两个无量纲的阶梯算符出发巧妙的推导出谐振子能量的本征值和本征矢,进而借用平移算符求解出谐振子的相干态.计算表明相干态表象的基矢是过完备的,同时在相干态中,坐标及其动量具有最小的不确定性. 相似文献
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本文在文献[1]的基础上研究了光子消灭算符高次幂αk(k≥3)的正交归一本征态的数学和量子统计性质,指出这些本征态均具有非经典效应,它们组成一个以非经典光场态作基矢的完备表象。在此之前,文献[1]讨论的k=3的情况只是我们所得普遍性结论的特例。
关键词: 相似文献
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The properties of the modified Pöschl–Teller potential are outlined. The ladder operators are constructed directly from the wave functions without introducing any auxiliary variable. It is shown that these operators are associated to the SU(2) algebra. Analytical expressions for the functions sinh(x) and (1/)cosh(x)d/dx are evaluated from these ladder operators. The harmonic limit for this system is discussed. The expansion of the coordinate x and the momentum p from the operators of the SU(2) are also obtained. 相似文献
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Some authors found that, in different coordinates, the tunneling approach gives different Hawking temperature for the Schwarzschild
black hole recently. In this paper, by studying the Hawking radiation of the Kerr black hole arising from the scalar and Dirac
particles, we find that, to obtain the Hawking temperature by using tunneling effect, the coordinate representations for the
stationary Kerr black hole should satisfy two conditions: (a) to keep the Killing vectors x(t)m{{\xi_{(t)}^\mu}} and x(j)m{{\xi_{(\varphi)}^\mu}} invariant; and (b) the radial coordinate transformation is a regular and non-zero function. 相似文献
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为了研究具有相互作用势和运动耦合的两个非全同的量子谐振子体系的动力学问题,利用有序算符乘积内的积分技术,建立了一种两粒子体系的组合坐标新表象|η1,η2〉,构造了一个双模压缩算符U并分析了其压缩特性. 应用组合坐标新表象严格求解了具有相互作用势和运动耦合的两个非全同的量子谐振子体系的动力学问题. 这为研究复杂耦合量子谐振子体系提供了一个有效途径.
关键词:
有序算符乘积内的积分技术
组合坐标表象
双模压缩算符
幺正矩阵 相似文献
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We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit coordinates and discuss the physical and dynamical picture. The isomorphism is then used as a base for the translation of the differential symplectic geometry of the infinite dimensional manifolds onto the observable algebra as a noncommutative geometry. Hence, we obtain the latter from the physical theory itself. We have essentially an extended formalism of the Schr̎odinger versus Heisenberg picture which we describe mathematically as like a coordinate map from the phase space, for which we have presented argument to be seen as the quantum model of the physical space, to the noncommutative geometry coordinated by the six position and momentum operators. The observable algebra is taken essentially as an algebra of formal functions on the latter operators. The work formulates the intuitive idea that the noncommutative geometry can be seen as an alternative, noncommutative coordinate, picture of familiar quantum phase space, at least so long as the symplectic geometry is concerned. 相似文献
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We construct a new mimetic tensor artificial viscosity on general polygonal meshes. The tensor artificial viscosity is based on discretization of coordinate invariant operators, divergence of a tensor and gradient of a vector. The focus of this paper is on the non-symmetric form, div(μ∇u), of the tensor artificial viscosity. The discretizations of this operator is derived for the case of a full tensor coefficient μ. However, in the numerical experiments, we only use scalar μ. We prove that the new tensor viscosity preserves spatial symmetry on special meshes. We demonstrate performance of the new viscosity for the Noh implosion, Sedov explosion and Saltzman piston problems on a set of various polygonal meshes in both Cartesian and axisymmetric coordinate systems. 相似文献
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In the context of molecular dynamics simulations of rare events, the application of constraints on a suitable reaction coordinate has often been found useful for sampling of the free energy barrier. The efficiency of these calculations is hampered by geometrical difficulties, related to the metric factor and inertial forces. Some years ago Mulders et al. [1996, J. chem. Phys., 104, 48691 suggested a way to simplify the approach. Their idea was demonstrated shortly afterwards by Sprik and Ciccotti [1998, J. chem. Phys., 109, 77371. The present paper extends these results to vector reaction coordinate and molecular systems modelled with holonomic constraints. 相似文献
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We show for a model system previously studied by Moiseyev et al. (1978, Molec. Phys., 36, 1613) how, with a basis of sufficient flexibility, the wave-function of the complex coordinate method can approach the function which can be directly obtained from a numerical integration of the wave equation with a complex coordinate and a complex energy. Diagrams of the complex wavefunction are used to visualize its behaviour in the short and long range regions, and the attenuation (localization) produced by the rotation. 相似文献