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Chinese Physics B 2010年第2期19卷 213-218页

作者：马宁王美山杨传路马晓光王德华 School of Physics and Electronic Engineering Ludong University

Employing the two-state model and the time-dependent wave packet method, we have investigated the influences of the parameters of the intense femtosecond laser field on the evolution of the wave packet, as well as the population of ground and double-minimum electronic states of the NaRb molecule. For the different laser wavelengths, the evolution of the wave packet of 6{ }^1／Sigma ^ ＋ state with time and internuclear distance is different, and the different laser intensity brings different influences on the population of the electronic states of the NaRb molecule. One can control the evolutions of wave packet and the population in each state by varying the laser parameters appropriately, which will be a benefit for the light manipulation of atomic and molecular processes.

关键词： intense femtosecond laser field time-dependent wave packet method wave packet population

The Structure and Propagation of Stationary Planetary wave packet in the Barotropic Atmosphere

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Advances in Atmospheric Sciences 1992年第2期9卷 157-166页

作者： Lu Peusheng LASG Institute of Atmospheric PhysicsAcademia SinicaBeijing

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their *** qualitative and quantitative analyses of equations of wave packet dynamics,which are obtained by the use of WKB approximation,are very helpful for the understanding of structure,formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the ***,these equations of wave packet dynamics can be directly solved by the method of characteristic lines,and the results can be simply and clearly interpreted by physical *** this paper,a quasi-geostrophic barotropic model is taken for simplicity,and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical *** is revealed that(a)the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small;(b)being superimposed on a westerly jet flow with positive shear(U_(λ)/y>0),the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere,then reach their maximum of amplitude at some critical latitude,and after that weaken again;(c)the connected line of extremes(the positive and negative centres)of wave packet does not coincide with but crosses the ray by an angle,the larger the scale of external forcing,the larger the angle;and(d)the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.

关键词： wave packet Basic Flow Trap wave Zonal wavenumber Zonal wave Number

Equivalence of String Classical and Quantum Energy beside Equivalence of wave packet and Relativistic Velocity in Eucleadian and Curved Space

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Natural Science 2020年第7期12卷 520-525页

作者： Mashair Ahmed Mohammed Yousif Abeer Mohammed Khairy Ahmed Zainab Mustapha Kurawa Omer A. M. Elnor Mubarak Dirar Abd-Alla Yagoub Ibrahim Mohammed Elfaki El-Tahir Mohammed Idriss Ahmed Zoalnoon Ahmed Abeid Allah Saad Department of Physics Faculty of Science and Education at Alkurma Taif University Alkhurma Kingdom of Saudi Arabia Department of Physics Faculty of Art and Science at Al Muznab Al Qassim University Al Muznab Kingdom of Saudi Arabia Department of Physics School of Science Education Saadatu Rimi College of Education Kumbotso Nigeria Department of Physics Faculty of Science University of Bakhtalruda Ed Dueim Sudan Department of Physics Faculty of Science Sudan University of Science and Technology Khartoum Sudan Department of Natural and Applied Sciences College of Science and Humanities at Afif Sharga University Afif Kingdom of Saudi Arabia College of Arts and Sciences King Khalid University Dhahran Saudi Arabia

Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.

关键词： Plank Energy Classical Energy String Quanta Photons Electromagnetic waves Curved Space Group Velocity wave packet

Where Is Phase Velocity in Minkowski Space?

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Journal of Modern Physics 2024年第10期15卷 1555-1566页

作者： Antony J. Bourdillon Ultra-High Resolution Lithography San Jose CA USA

In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: *** = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ,

关键词： Event Horizon Scattering Range wave packet Phase Velocity Group Velocity Dispersion Dynamics Quantum Physics

Physical interpretation of Planck's constant based on the Maxwell theory

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Chinese Physics B 2017年第4期26卷 87-95页

作者：张东才 Macro-Science Group Division of LIFSHong Kong University of Science and TechnologyClear Water BayHong KongChina

The discovery of the Planck relation is generally regarded as the starting point of quantum ***＇s constant h is now regarded as one of the most important universal *** physical nature of h,however,has not been well *** was originally suggested as a fitting constant to explain the black-body *** Planck had proposed a theoretical justification of h,he was never satisfied with *** solve this outstanding problem,we use the Maxwell theory to directly calculate the energy and momentum of a radiation wave *** find that the energy of the wave packet is indeed proportional to its oscillation *** allows us to derive the value of Planck＇s ***,we show that the emission and transmission of a photon follows the all-or-none *** ＂strength＂ of the wave packet can be characterized by ζ,which represents the integrated strength of the vector potential along a transverse *** reason that ζ should have a fixed cut-off value for all *** results suggest that a wave packet can behave like a *** offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by Planck＇s law.

关键词： Planck's constant Maxwell's theory de Broglie relation uncertainty principle wave packet photon

Autler-Townes splitting in photoelectron spectra of K_2 molecule

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Chinese Physics B 2012年第2期21卷 259-265页

作者： Yao Hong-Bin Zheng Yu-Jun School of Physics Shandong UniversityJinan 250100China

We investigate Autler-Townes splitting in the photoelectron spectra of K2 molecule driven by pump-probe pulses via employing the time-dependent wave packet approach. It is found that the magnitude of Aulter-Townes splitting varies with the wavelength of the intense laser pulse. In particular, the phenomenon of Aulter-Townes splitting vanishes for the far-off resonance of the pump pulse. Also, the split peaks of Autler Townes in the case of resonant pump pulse give us an approach to directly obtaining the transition dipole moment of a molecule.

关键词： Autler-Townes splitting photoelectron spectra K2 molecule wave packet

Relativistic Dynamics, Electromagnetic Field,and Spin, as All Quantum Effects

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Journal of Electronic Science and Technology 2017年第4期15卷 333-341页

作者： Eliade Stefanescu Center of Advanced Studies in Physics Bucharest 050711 Romania Institute of Mathematics “Simion Stoilow” of the Romanian Academy Bucharest 010702 Romania

We consider a quantum particle as a wave packet in the coordinate space. When the conjugate wave packet in the momentum space is considered, we find that the group velocities of these two wave packets, which describe the particle dynamics, are in agreement with the Hamilton equations only if in the time dependent phases one considers the Lagrangian instead of the Hamiltonian which leads to the conventional Schr?dinger equation. We define a relativistic quantum principle asserting that a quantum particle has a finite frequency spectrum, with a cutoff propagation velocity c as a universal constant not depending on the coordinate system, and that any time dependent phase variation is the same in any system of coordinates. From the time dependent phase invariance,the relativistic kinematics is obtained. We consider two types of possible interactions: 1) An interaction with an external field, by a modification of the time dependent phase differential with the terms proportional to the differentials of the space-time coordinates multiplied with the components of this field four-potential, and 2)an interaction by a deformation of the space-time coordinates, due to a gravitational field. From the invariance of the time dependent phase with field components, we obtain a mechanical force of the form of Lorentz’s force, and three Maxwell equations: The Gauss-Maxwell equations for the electric and magnetic fluxes, and the Faraday-Maxwell equation for the electromagnetic induction. When the fourth equation,Ampère-Maxwell, is considered, the interaction field takes the form of the electromagnetic field. For a low propagation velocity of the particle waves, we get a packet of waves with the time dependent phases proportional to the relativistic Hamiltonian, as in Dirac’s famous theory of spin, and a slowly-varying amplitude with a phase proportional to the momentum and this velocity. In the framework of our theory, the spin is obtained as an all quantum effect, without any additio

关键词： Group velocity Maxwell equations metric tensor quantum particle spin wave packet

Scalar optical hopfions

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eLight 2022年第1期2卷 284-290页

作者： Chenhao Wan Yijie Shen Andy Chong Qiwen Zhan School of Optical‑Electrical and Computer Engineering University of Shanghai for Science and TechnologyShanghai 200093China School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics Huazhong University of Science and TechnologyWuhan 430074HubeiChina Optoelectronics Research Centre University of SouthamptonSouthampton SO171BJUK Department of Physics Pusan National UniversityGeumjeong‑GuBusan 46241South Korea Zhangjiang Laboratory 100 Haike RoadShanghai 201204China Shanghai Key Lab of Modern Optical System University of Shanghai for Science and TechnologyShanghai 200093China

Hopfions are three-dimensional(3D)topological states discovered in field theory,magnetics,and hydrodynamics that resemble particle-like objects in physical *** inherit the topological features of the Hopf fibration,a homotopic mapping from unit sphere in 4D space to unit sphere in 3D *** we design and demonstrate dynamic scalar optical hopfions in the shape of a toroidal vortex and expressed as an approximate solution to Maxwell’s *** lines correspond to disjoint and interlinked loops forming complete ring tori in 3D *** Hopf invariant,product of two winding numbers,is determined by the topological charge of the poloidal spatiotemporal vortices and toroidal spatial vortices in toroidal *** hopfions provide a photonic testbed for studying topological states and may be utilized as high-dimensional information carriers.

关键词： Hopfion Toroidal vortex Spatiotemporal vortex wave packet Topology Topological charge

ON THE SYMMETRIC DEVELOPMENT OF MESOSCALE DISTURBANCES

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Acta meteorologica Sinica 1991年第2期5卷 197-203页

作者：孙立潭赵瑞星 Institute of Atmospheric Physics Academia SinicaBeijing

The effects of baroclinic basic flow on a paralleled mesoscale disturbance development are investigated. By using the WKB method,two-dimensional perturbation equations with the anelastic approximation are *** result indicates that the symmetric development of a mesoscale disturbance is due to the in- homogeneous thermal wind deviations and unstationality of the basic field.

关键词： baroclinic atmosphere wave packet symmetric development mesoscale disturbance thermal wind deviation

Quantum Mechanics: Harmonic wave-packets, Localized by Resonant Response in Dispersion Dynamics

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Journal of Modern Physics 2023年第2期14卷 171-182页

作者： Antony J. Bourdillon UHRL San Jose USA

From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.

关键词： wave packet Reduction Phase Velocity Hidden Variables Young’s Slits Resonant Response Dispersion Dynamics Quantum Physics