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含时阻尼线性谐振子的量子不变量处理 总被引:1,自引:0,他引:1
在适当的正则化变换下,采用Lewis-Riesenfeld量子不变量理论,得到了含时阻尼线性谐振子的精确波函数,波函数的正确性和普遍性同样得到讨论. 相似文献
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通过正则化变换技巧,寻找到一种对阻尼系数随时间变化的阻尼谐振子直接量子化方案,进而采用高斯型传播子和费曼路径积分方法求出了含时阻尼谐振子的严格波函数,并对波函数的普遍意义,坐标和动量的零点涨落以及两者的不确定关系作了讨论
关键词:
含时阻尼
传播子
费曼路径积分 相似文献
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我们研究了量子光学理论中的宇称算符及其应用。我们用有序算符内的积分方法,从宇称变换的物理意义出发自然地导出量子宇称算符的明确表达式;并将宇称变换和其它量子变换(如坐标-动量互变、压缩变换等)结合在一起考虑,构建了联合变换算符。最后给出了宇称算符在构建共轭纠缠态表象的应用。 相似文献
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关于量子力学中正则对易关系与对应原理自洽性的讨论 总被引:2,自引:2,他引:0
正则对易关系与对应原理是从经典力学建立量子力学的数学体系所必须遵守的两个基本假定.正则对易关系决定了坐标与动量算符的具体形式.例如,从直角坐标与动量算符的对易关系即可得出在坐标表象中至于一般力学量的算符形式,则由对应原理给出.例如,设某经典力学量为F(x,px)(总可表为直角坐标与动量的函数),如将x与px分别换成x与px(当然要按一定的规则厄米化),就得到量子力学中相应的力学量算符F(x,px).特别是,由于经典力学中的广义坐标(一般为曲线坐标)及其共轭动量均可表为直角坐标与动量的函数,那么量子力学中,相应的广义坐标及其共轭动量… 相似文献
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量子非局域关联是量子理论最基础的特征之一.“X”态作为实验中常见的一种量子态,因其在演化过程中仍保持“X”形的稳定性,而被广泛应用于开放量子系统的研究中.利用Clauser-Horne-Shimony-Holt (CHSH)不等式,在Markov环境这种典型的开放量子系统下,研究了两种通过局部变换操作所关联的“X”态在振幅阻尼环境和相位阻尼环境中量子非局域检验结果随时间的演化情况.研究结果表明,在相位阻尼环境中,随着演化时间的增加,两种“X”态具有相同的CHSH不等式检验结果.在振幅阻尼环境中,利用局部变换操作得到的“X”态,可获得较长的成功进行量子非局域关联检验的演化时间.最后,详细给出了两种类型“X”态在相位阻尼环境和振幅阻尼环境中成功进行量子非局域关联检验的保真度范围. 相似文献
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轻阻尼振子的经典力学处理和量子力学处理 总被引:5,自引:2,他引:3
本文讨论了对于微观轻阻尼(β/ω1<<1)振子体系,借助正则化变换技巧,可采用通常简便的量子力学方法进行处理.其结果表明了体系的量子效应,既与始值条件相关,且又随阻尼按指数规律(e~(-2βt))衰减.量子力学的处理方法和结果均与经典力学处理呈显明的对应关系. 相似文献
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V. P. Koshcheev D. A. Morgun T. A. Panina 《Bulletin of the Russian Academy of Sciences: Physics》2009,73(11):1491-1495
A system of equations describing the evolution of the mean-square quantum fluctuations of the transverse coordinate and momentum
operators and the evolution of the mean-square fluctuations of the transverse coordinate and momentum with respect to the
classical trajectory of channeled particle is constructed using linearized Heisenberg equations. The energy losses of channeled
particles on crystal electrons and the mean-square fluctuations of the transverse coordinate and momentum are calculated within
the same formalism. 相似文献
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No Heading A hydrodynamic analogy for quantum mechanics is used to develop a phase-space representation in terms of a quasi-probability distribution function. Averages over phase space using this approach agree with the usual expectation values of quantum mechanics for a certain class of observables. We also derive the equations of motion that particles in an ensemble would have in phase space in order to mimic the time development of this probability distribution, thus giving the position and momentum of particles in the ensemble as a function of time. The equations of motion separate into position and momentum components. The position component reproduces the de Broglie-Bohm equation of motion. As a simple example, we calculate the phase space trajectories and entropy of a free particle wave packet. 相似文献
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The formalism of Luo [Int. J. Theor. Phys. 41 (2002) 1713] on local values of quantum observables is generalized for N-electron systems both in coordinate and momentum spaces. It is shown that the imaginary part of the total local coordinate (momentum) is the half of the local wave vector (or the half of the gradient of the local momentum(coordinate)-space Shannon information per particle). 相似文献
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We calculate zero temperature Green’s function, the density–density correlations and expectation values of a one-dimensional quantum particle which interacts with a Fermi-sea via a δ-potential. The eigenfunctions of the Bethe-Ansatz solvable model can be expressed as a determinant. This allows us to obtain a compact expression for the Green’s function of the extra particle. In the hardcore limit the resulting expression can be analyzed further using Painlevé V transcendents. It is found that depending on the extra particles momentum its Green’s function undergoes a transition of that for hardcore Bosons to that of free Fermions. 相似文献
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Quantum matrix elements of the coordinate, momentum and the velocity operator for a spin-1/2 particle moving in a scalar-like
potential are calculated. In the large quantum number limit, these matrix elements give classical quantities for a relativistic
system with a position-dependent mass. Meanwhile, the Klein-Gordon equation for the spin-0 particle is discussed too. Though
the Heisenberg equations for both the spin-0 and spin-1/2 particles are unlike the classical equations of motion, they go
to the classical equations in the classical limit.
相似文献
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Eduard Prugovečki 《Foundations of Physics》1981,11(5-6):355-382
A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.Supported in part by an NSERC grant. 相似文献
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《Nuclear Physics B》1998,511(3):737-759
The weak energy condition is known to fail in general when applied to expectation values of the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states |ψ〉 for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on |ψ〉 is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of the scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non-trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on |ψ〉 are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories. 相似文献
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Xiao-feng Pang 《Frontiers of Physics in China》2008,3(2):205-237
In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems
in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear
quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of
the solution of the nonlinear Schr?dinger equation, the stability of microscopic particles described by NLQM, invariances
and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and
Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the
features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as
well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass,
energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws
of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of
motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They
have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule
of motion and conservation laws of energy, momentum and mass, satisfy minimum uncertainty relation, can be localized due to
the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that
rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical
theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic
particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence,
the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance
and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum
mechanics has extensive applications in physics, chemistry, biology and polymers, etc.
相似文献
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PANG Xiao-feng 《Frontiers of Physics》2008,3(2):205
In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy,momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence, the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum mechanics has extensive applications in physics, chemistry, biology and polymers, etc. 相似文献
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L. J. Landau 《Journal of statistical physics》1994,77(1-2):259-309
A quantum particle observed on a sufficiently large space-time scale can be described by means of classical particle trajectories. The joint distribution for large-scale multiple-time position and momentum measurements on a nonrelativistic quantum particle moving freely inR
v is given by straight-line trajectories with probabilities determined by the initial momentum-space wavefunction. For large-scale toroidal and rectangular regions the trajectories are geodesics. In a uniform gravitational field the trajectories are parabolas. A quantum counting process on free particles is also considered and shown to converge in the large-space-time limit to a classical counting process for particles with straight-line trajectories. If the quantum particle interacts weakly with its environment, the classical particle trajectories may undergo random jumps. In the random potential model considered here, the quantum particle evolves according to a reversible unitary one-parameter group describing elastic scattering off static randomly distributed impurities (a quantum Lorentz gas). In the large-space-time weak-coupling limit a classical stochastic process is obtained with probability one and describes a classical particle moving with constant speed in straight lines between random jumps in direction. The process depends only on the ensemble value of the covariance of the random field and not on the sample field. The probability density in phase space associated with the classical stochastic process satisfies the linear Boltzmann equation for the classical Lorentz gas, which, in the limith0, goes over to the linear Landau equation. Our study of the quantum Lorentz gas is based on a perturbative expansion and, as in other studies of this system, the series can be controlled only for small values of the rescaled time and for Gaussian random fields. The discussion of classical particle trajectories for nonrelativistic particles on a macroscopic spacetime scale applies also to relativistic particles. The problem of the spatial localization of a relativistic particle is avoided by observing the particle on a sufficiently large space-time scale. 相似文献