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1.
H.A. Tolhoek 《Physica A》1975,81(4):535-564
In this paper a generalization of the traditional non-relativistic Schrödinger equation is considered. It is a wave equation of second order in time and fourth order in the space coordinates for scalar fields. The equation has certain features, which make it a closer analogue of the Klein-Gordon equation than the traditional Schrödinger equation. However, the equation maintains the non-relativistic relation between energy and momentum.The implications of this generalized wave equation and the quantized field theory based on it are studied. The theory can be shown to be charge symmetric and allows to introduce anti-particles and pair creation. We compare the Green functions for this theory with those of conventional non-relativistic quantum theory.The theory allows to formulate a transformation for charge conjugation. The PCT-theorem is valid for it. The usual spin-statistics connection holds.  相似文献   

2.
We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections.  相似文献   

3.
黄万霞  王一  许新胜 《大学物理》2023,42(1):30-34+41
被广泛地用于力学、光学、电学等相关学科中的时域耦合模理论,在前沿科学研究中扮演着越来越重要的角色.在教学和科研相结合的本科教学理念下,将时域耦合模理论引入“理论力学”中已刻不容缓.本文结合拉格朗日方程和久期微扰理论,将振子耦合的二阶微分方程退化为一阶微分方程,即时域耦合模理论的主方程.该探究为本科生顺利接受时域耦合模理论提供了一种方案,并且在本科生素质培养方面有一定的意义.  相似文献   

4.
The non-linear flux equation, the non-linear Fokker-Planck equation (or Smoluchowski equation), and the non-linear Langiven equation are the basicequations for describing particle diffusion in non-ideal system subjected totime-dependent external fields. Nevertheless, the exact solution of thoseequations is still a challenge because of their inherent complexity of thenon-linear mathematics. Li et al. found that, based on the defined apparentvariables, the non-linear Fokker-Planck equation and the non-linear flux equation could be transformed to linear forms under the condition of strong friction limit or local equilibrium assumption. In this paper, some new features of the theory were found: (i) The linear flux equation for describing non-linear diffusion can be obtained from the irreversible thermodynamic theory; (ii) The linear non-steady state diffusion equation for describing non-linear diffusion of the non-steady state, which was described by the non-linear Fokker-Planck equation, can be derived more consistently from the microscopic molecular statistical theory; (iii) In the theory, thenon-linear Langiven equation also bears a linear form; (iv) For some special cases, e.g. diffusion in a periodic total potential system, the local equilibrium assumption or the strong friction limit is not required in establishing the linear theory for describing non-linear diffusion, so the linear theory may be important in the study of Brown motor.  相似文献   

5.
刘卫平  席德科  杨新铁 《光子学报》2008,37(6):1250-1254
从可压缩连续介质角度出发,给出一种可以在空间二级准确度上兼容的相对论然而又允许超光速介质运动存在的数学描述.先给出无粘不可压缩流动的Euler方程可以改写成和电磁场方程相同的表达形式:在空间二阶准确度的意义上来说,不可压缩流+相对论近似等于可压缩流,它们都是和现在的实验结果相融的;给出可压缩流动的广义相对论.这也说明协变不变原理不过是可压缩流动的一种近似处理方法.新模型可以解释索么菲(A.Sommerfeld)提出的粒子在超过光速后减小能量反而加速的现象.  相似文献   

6.
We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibronic and electron-electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green's function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.  相似文献   

7.
模耦合理论比较成功地解释了微波不稳定性的发生,其理论基础是Vlasov方程.Fokker-Planck方程包含了束团的辐射阻尼效应和量子激发效应,是比较完备地描述粒子运动状态的束团分布方程.比较了Fokker-Planck方程和Vlasov方程在来源、意义和解法方面的关联和不同,同时介绍了一种多项式展开束团耦合模式来求解Fokker-Planck方程的方法,并在静态分布中包含了势阱畸变的效应.  相似文献   

8.
SAFT-dimer (SAFT-D) theory is reformulated to yield an improved equation of state for the hard sphere chain fluid. Two sets of the equation of state are proposed by employing Chiew's expressions for the contact values of the m hard sphere site-site correlation function g(σ). Comparison with molecular simulation data shows that the improved SAFT-D equation of state predicts the compressibility factor more accurately than Ghonasgi and Chapman's equation of state. It has been shown that SAFT-dimer theory can be applied readily to fused hard sphere chain fluids by considering the correct value of the effective chain length (m*). SAFT-dimer theory is also extended to the 2-dimensional tangent and fused hard disc chain fluids. For the fused hard disc dimer fluid, the SAFT equation of state is found to be more accurate than the Boublik hard disc dimer equation of state. For tangent hard disc chain fluids, the results obtained from SAFT-dimer theory are compared with Monte Carlo results for 5-mers and with GFD theory for 4-mers, 8-mers and 16-mers.  相似文献   

9.
何祚庥  黄涛 《物理学报》1974,23(2):33-72
本文引进了双粒子的双重定域场算符和Bethe-Salpeter的算子方程来描述复合场的运动和变化,进一步扩展了H-N-Z的束缚态场论。  相似文献   

10.
A generalized Schrödinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained by considering the internal complex structure of the particle which is a consequence of stochastic average of particle oscillations in the zeropoint field. Hence, the generalised Schrödinger equation may be called stochastic Schrödinger equation. It is found that the second order correction terms are similar to corresponding relativistic corrections. When higher order correction terms are neglected, the stochastic Schrödinger equation reduces to normal Schrödinger equation. It is found that the Schrödinger equation contains an internal structure in disguise and that can be revealed in the form of internal kinetic energy. The internal kinetic energy is found to be equal to the quantum potential obtained in the Madelung fluid theory or Bohm statistical theory. In the rest frame of the particle, the stochastic Schrödinger equation reduces to a Dirac type equation and its Lorentz boost gives the Dirac equation. Finally, the relativistic Klein–Gordon equation is derived by squaring the stochastic Schrödinger equation. The theory elucidates a logical understanding of classical approach to quantum mechanical foundations.  相似文献   

11.
Using published results on continuous time random walk theories, we show that the random walk theory of Gissler and Rother is equivalent to a master equation with jumps to further neighbor sites. We extend the theory to include time correlations over two jumps. No special assumptions are made in the analysis, so that the theory may be applied to any lattice type with a general time probability distribution for jumps; a generalized second-order differential equation is given for the results. In the special case of an exponential time probability density, a simple homogeneous second order differential equation is obtained which is shown to be equivalent to a certain two-state master equation model.  相似文献   

12.
It is demonstrated that the kinetic equation of Davis's effective potential theory follows directly from the application of well-defined approximations to the three-body correlations involved in the second equation of the BBGKY hierarchy. The same, simple mathematical techniques involved in this demonstration are used to derive two other kinetic equations, one of which is a generalization to high densities of the Boltzmann equation. In order to facilitate its application to the calculation of the van Hove and other correlation functions, the kinetic equation of the effective potential theory is Fourier-Laplace transformed: explicit formulae are given for the matrix elements of all operators that occur in this equation.  相似文献   

13.
We propose a new approach to transport of the suspensions and tracers in porous media. The approach is based on a modified version of the continuous time random walk (CTRW) theory. In the framework of this theory we derive an elliptic transport equation. The new equation contains the time and the mixed dispersion terms expressing the dispersion of the particle time steps. The properties of the new equation are studied and the fundamental analytical solutions are obtained. The solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward “tail” contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions of the CTRW theory.  相似文献   

14.
纳米量级超导Al粒子在磁场中的Zeeman分裂   总被引:4,自引:0,他引:4       下载免费PDF全文
用随机矩阵理论对BCS理论中的自洽方程进行修正.由此得到的新自洽方程能合理地描述纳米量级Al粒子的超导电性.更进一步论证在外磁场作用下,s>0态由于Zeeman效应得出了实验中已观测到的超导增强效应. 关键词: 纳米粒子 超导电性 Zeeman分裂  相似文献   

15.
马文秀  周德堂 《物理学报》1993,42(11):1731-1734
修正了文献[5]中推广的KdV方程传播波解的形变理论,并提出了一个相关的代数方程有非零实根的充要条件,从而指出了文献[5]中的一个分析错误。最后直接从推广的KdV方程本身给出了由形变理论生成的孤波解的显式公式。 关键词:  相似文献   

16.
A new memoryless expression for the equation of motion for the reduced density matrix is derived. It is equivalent to that proposed by Tokuyama and Mori, but has a more convenient form for the application of the perturbational expansion method. The master equation derived from this form of equation in the first Born approximation is applied to two examples, the Brownian motion of a quantal oscillator and that of a spin. In both examples the master equation is rewritten into the coherent-state representation. A comparison is made with the stochastic theory of the spectral line shape given by Kubo, and it is shown that this theory of the line shape can be incorporated into the framework of the present theory.  相似文献   

17.
李建清  莫元龙 《物理学报》2006,55(8):4117-4122
在同时考虑多信号输入和相对论效应的情况下,利用波导激励理论获得了行波管中慢电磁行波与电子注非线性互作用的全三维自洽工作方程组,包括激发方程、运动方程、能量转化方程、相位演化方程等,适合大部分行波管中慢电磁行波与电子注的非线性互作用过程.利用该理论具体分析了一个宽带螺旋线行波管在多信号输入时的交叉调制,并与实验结果进行了比较,验证了理论和计算的正确性.另外,还模拟了一个相对论盘荷波导行波管中的非线性注波互作用过程. 关键词: 行波管 慢电磁行波 非线性注波互作用 交叉调制  相似文献   

18.
WU Ning   《理论物理通讯》2007,48(9):469-472
In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannot be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field,an equation of motion of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.  相似文献   

19.
WU Ning 《理论物理通讯》2007,48(3):469-472
In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannog be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field, an equation of motlon of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.  相似文献   

20.
在本文中,作者推得一组相对论式的汉密尔敦运动式;并根据此运动式,详细地讨论了一质点之运动;由此还可以很自然地看出,在量子力学中,狄拉克电子方程式似乎是一个必然的波动方程式。在狄拉克理论中的取平方根步骤在这里找到它在古典物理学中的对照。同时根据了上面的理论,作者还推得到一个相对论式的哈生堡方程式,最后则讨论了此方程式在狄拉克电子理论中的一些应用;同时并指出,在相对论的观点上,此方程式可以引导出一些比较对称的及有比较普遍形式的物理的量。  相似文献   

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