Klein-Gordon方程Q球解中能量稳定性和扰动研究

本文研究了一种复标量场模型中的双层Q球解,在解析形式下计算了Q球荷和能量. 同时,分析了其能量稳定性质,通过Klein-Gordon 方程获得了Q球能量的扰动表达式. 另外,还讨论了Q球暗物质产生的物理效应. 关键词： Klein-Gordon方程 Q球解 能量稳定性与扰动 暗物质     

Klein-Gordon thermal equation for a planck gas

In this paper the quantum hyperbolic equation formulated in our earlier paper [Found. Phys. Lett. 10, 599 (1997)] is applied to the study of the propagation of the initial thermal state of the universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced,V _P = ħ/8t_P = 1.125 10¹⁸ GeV, wheret _P is a Planck time. For the barrier heightV <V _P , the master thermal equation isthe modified telegrapher’sequation, and for barrier heightV >V _P the master equation is theKlein- Gordon equation. The solutions of both type equations for Cauchy boundary conditions are discussed.     

Fitzhugh-Nagumo nerve conduction equation: A singular perturbation analysis

A singular perturbation theory is applied to the FitzHugh-Nagumo nerve conduction equation with quadratic nonlinearity to obtain travelling pulse profiles. Starting with the zeroth-order pulse solution, the explicit first-order correction to the propagating pulses is obtained.     

Gravitational perturbation of the Klein-Gordon excited states

The gravitational perturbation of the excited states of the Klein-Gordon particle moving in a closed box is calculated. The result obtained is used to estimate the magnitude of the gravitational perturbation of energy levels of meson states.     

A wave operator for a non-linear Klein-Gordon equation

We prove the existence of a set of initial data to which correspond solutions of the nonlinear Klein-Gordon equation with a polynomial nonlinear term, which converge asymptotically, when t→+∞, to solutions of the linear Klein-Gordon equation.     

Anharmonic solution of Schrödinger time-independent equation

We present here a mathematical explanation of how the Schr?dinger equation for a class of harmonic oscillators possesses exact solutions. Some of the extended potentials used here are not present in the literature.     

Progress in a trajectory interpretation of the Klein-Gordon equation

A trajectory interpretation is developed for the Klein-Gordon equation in one dimension. The development is couched in a Hamilton-Jacobi representation. Equations of motion are developed. Different trajectories for a given eigenvalue energy are shown to manifest different microstates of the eigenfunction of that particular energy.     

The Klein-Gordon equation and scattering theory

Using our previously developed theory, we prove the main conclusions of scattering theory for the Klein-Gordon equation under hypotheses weaker than presently known. We consider more general equations and obtain stronger results.     

Photon velocity from the Klein-Gordon equation

An approximate mathematical relationship for the velocity of a photon as a non-zero rest-mass quantum particle is derived from the field-free Klein-Gordon equation in the framework of the de Broglie-Bohm theory of quantum mechanics.     

The Klein-Gordon equation with light-cone data

It is shown that the characteristic Cauchy problem ·u(x,t)=0,u(x,–|x|)=f(x),x ⁿ ,n1 has a unique finite energy weak solution for allf such that dx(|f|²+|f|²)< and all finite energy weak solutions of the equation are obtained in this way.     

用克莱因-戈登方程推导两质子之间的库仑势

量子电动力学认为库仑力是电荷之间交换虚光子的结果,最有力的证据是从虚光子假说直接推出库仑势能.克莱因-戈登方程(□2-m2)Φ(x,t)=0是一个用来描述质量为m,自旋为0,电荷为0的标量场的场方程,虚光子可以用粒子静止质量为0的标量场描述,因此满足克莱因-戈登方程□2Φ(x,t)=0.本文利用克莱因-戈登方程推导两质子之间的库仑势.     

The Klein-Gordon equation as a limiting case of a suitably hyperbolized schrödinger equation

We obtain a hyperbolic equation whose discontinuity waves are all exceptional and propagate with velocity λ. When λ → ∞ or λ=c, this equation becomes identical to the Schrödinger equation and to the Klein-Gordon equation respectively. We also show that λ is related to the dispersion relationE(p).     

Charge-magnetic-dipole bound states using the Klein-Gordon equation

We investigate bound states of a composite system consisting of a charged particle orbiting a neutral, stationary magnetic dipole. We find all bound states are metastable and none exist with angular momentum less than eleven. Our calculations is performed in two space dimensions.     

Generalized virial theorem for the Klein-Gordon equation

The virial theorem for the Klein-Gordon equation has been generalized with respect to non-integrable scale-invariant probe functions. Ground-state energies as well as certain upper bounds on the coupling constants have been established. For definiteness several kinds of attractive power potentials have been considered.     

The Klein-Gordon equation in some anisotropic cosmologies

The Klein-Gordon equation is studied in a family of exact solutions of the Einstein equations whose material content is a perfect fluid with stiff equation of state (p=). The field equations are solved exactly for some members of the family and for massive or massless fields.     

Trajectory length constraint and the Klein-Gordon equation

It is shown that the relativistic constraint of the length of possible trajectories in the method of integrals over the trajectories results in the Klein-Gordon equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 63–65, December, 1984.     

Causal interpretation of the modified Klein-Gordon equation

A consistent causal interpretation of the Klein-Gordon equation treated as a field equation has been developed, and leads to a model of entities described by the Klein-Gordon equation, i.e., spinless, massive bosons, as objectively existing fields. The question arises, however, as to whether a causal interpretation based on a particle ontology of the Klein-Gordon equation is also possible. Our purpose in this article will be to indicate, by making what we believe is a best possible attempt at developing a particle interpretation of the Klein-Gordon equation, that such an interpretation is untenable. To resolve the nonpositive-definite probability density difficulties with the Klein-Gordon equation, we modify this equation by the introduction of an evolution parameter. We base our subsequent considerations on this modified Klein-Gordon equation. Partly to motivate the need for a relativistic causal interpretation and partly to give emphasis to aspects of the causal interpretation often overlooked, we begin our article with a brief historical survey of the causal interpretation.Other work commitments prevented publication of this article in the special issue ofFoundations of Physics in honor of Prof. J. P. Vigier. I would nevertheless like to dedicate this work to Prof. Vigier in recognition of this untiring contributions to the causal interpretation in particular and to the foundations of physics in general. I take this opportunity to thank Prof. Vigier for his help during my Royal Society fellowship spent at the Institut Henri Poincaré in the academic year 1988–1989.