Modelling of elementary particles is a very important question in contemporary physics, in fact in the absence of a real physical representation, due to smallest sizes of particles, the identification of suitable models becomes necessary. It is known that postmodern physics is characterized still by the indeterministic dualism wave-corpuscle that prevents to give an unequivocal identity to elementary particles as per the obsolete paradigm: is the particle wave or corpuscle? or: is the particle at the same time wave and corpuscle? Research of suitable and coherent models is therefore fundamental in contemporary physics and it can give an important contribution also to the solution of the present problem relative to the physical phenomenon of oscillation that regards neutrino but also all other elementary particles.
Modelling of elementary particles is a very important question in contemporary physics, in fact in the absence of a real physical representation, due to smallest sizes of particles, the identification of suitable models becomes necessary. It is known that postmodern physics is characterized still by the indeterministic dualism wave-corpuscle that prevents to give an unequivocal identity to elementary particles as per the obsolete paradigm: is the particle wave or corpuscle? or: is the particle at the same time wave and corpuscle? Research of suitable and coherent models is therefore fundamental in contemporary physics and it can give an important contribution also to the solution of the present problem relative to the physical phenomenon of oscillation that regards neutrino but also all other elementary particles.
The contents of the article is mirrored in its title. In science the fact is well-known, that often opposite notions about that or diverse phenomenon result in identical end results, that produces bitter controversies of the opponents. The example can be served by century dispute between the supporters of the wave and corpuscular nature of light, dispute between a system of Ptolemy and Copernicus and many other conflictings in the most miscellaneous areas of science. The wave description of physical phenomena cannot be executed without of elastic medium (ether) in which one there is a wave process and is diffused by means of this elastic medium. Therefore description of wave phenomena in a solid, liquid and gas adequately mirrors the test datas and problems here does not arise. There, where the elastic medium misses, it is necessary to invent miscellaneous ruses to distribute the wave description and to these objects: empty world space (world ether in the miscellaneous fancy forms), internal space of atoms (wave functions of probability), fields (short-range interaction of fields by means of transfer of a disturbance from one point to other), electromagnetic radiation of the Maxwell (simultaneous oscillation magnetic and electrical field in an elastic medium). The wave description of world is fine is designed, since above it many generations of the known scientists worked, but main brake here it is necessary to have in stock an elastic medium. There, where it no or there are doubts in its existence, a field for critics there is opened. In the formal-mathematical description of the world the elastic medium is not necessary any more. Record a wave equation and decide it for the diversified cases. Though in mathematical relation such description of the world perfectly, but the physical sense of mathematical manipulations is lost. Specially it notably in a quantum mechanics. As a consequence, the similar description it is easy to subject a severe critic. To be salvaged from of intrusive critics, it is necessary to invent completely fancy notions about a microcosmos, which one do not have conformity in a macroworld. Thus, the unity of the world is upset, that directly contradicts fundamental laws of universe. The absence of physical sense is the main unremovable brake of the formal-mathematical description of the world. The corpuscular description of the world, basically, is a merit of Newton. Because of small number of the supporters of such description «have defeated» wave notions. The main brake for of corpuscular world was established by Newton, by formulating the law even and rectilinear motion of free bodies. This law has become force majeure for explanation of an interference, polarization and some other properties of light. Attempts to mate the wave description with corpuscular (wave-corpuscle dualism of microparticles [1]) are originally doomed on a fall because of a principled difference between a wave and particle. The ether is not necessary for the corpuscular description of the world in any to the form, therefore photon, for example, billions of years not «being spread» can move in space, that is impossible from the point of view of the wave description of its motion. The main lack of the corpuscular description of the world consists in incompletness of official toolkit for such description. Only new corpuscular quantum physics has entered notion about originating of a gravidynamic field at motion of gravitational charges and bound with this fact by screw motion of free bodies. It has allowed to revise many fundamental rules of classic physics and quantum mechanicses and to realise a capability of the corpuscular description of the world to the full. Unfortunately, it has taken place after in heads of the scientists strongly was fixed paradigm, designed Einstein and fathers of a quantum mechanics. This paradigm had time knock home in heads of millions students and even of the homemakers. In outcome new scientific paradigm on the basis of new physics meets aggressive hostility. It, certainly, temporary phenomenon and the victory new paradigm in science is foregone, as was already repeatedly. It is a pity, that this the temporary interval, usually, exceeds temporary existence of the person in the land of the living, and orthodoxes permanently self-reproduction by conservative science.
Introduction The evolution of microelectronics toward reduced device sizes has proceeded to a degree that renders conventional models, approaches, and theories inapplicable. Indeed, for objects with sizes of 100 nanometers or less it is frequently the case that the length scales associated with fundamental physical processes are comparable to the geometrical size of the device; also, fundamental time scales associated with physical processes are of the order of the time parameters for nanodevice operation. Therefore, on the nanoscale the theories and models underlying modern nanoelectronics become more complicated, and rely more and more on basic science. Generally, in the nanoworld the fundamental laws of physics that govern particles and material fields differ from those that apply to familiar macroscopic phenomena such as the motion of a baseball or a train. Instead of classical mechanics, that works so well for macroscopic phenomena, the motion of particles in the nanoworld is determined by the so-called wave mechanics or quantum mechanics. An underlying principle of central importance for nanophysics is the fundamental concept that all matter , including electrons, nuclei, and electromagnetic fields, behaves as both waves and particles , that is, wave–particle duality is a basic characteristic of all matter. At first glance, wave properties and particle properties for the same physical object are hardly compatible. To understand wave–particle duality, we will briefly review, in the following two subsections, the basic properties of particles and waves known from classical physics.
The basic concepts of space and time have undergone radical changes in the course of history, which render the Newtonian notions of elementary particles obsolete. This was inherent in the formulations of quantum mechanics, as the zitterbewegung of quantum-mechanical free particles are not the same as that of classical ones. The quantum field theories do not fare any better as particles and the corresponding fields are inseparable concepts. As physical concepts are becoming fuzzy, the definition of what constitutes an experimental "discovery" of an elementary particle is being revised. In these attempts, the quasi-particles, which are simple mathematical conveniences, tend to be reclassified as physical entities. The current model depictions of physical vacuum as superconducting medium do not accommodate a picture of elementary particles as individual entities. It is a situation where interactions and interactants become entangled and description of either one independent of the other is unattainable.
原有量子力学的由Schrodinger方程不能很好地描述微观粒子的局域特性和波-粒二象性，因此，量子力学必须改进和发展。在非线性系统中我们考虑了粒子之间或它与背景场之间的非线性相互作用，于是必须用非线性Schrodinger方程去描述的微观粒子的状态。至此，微观粒子的状态和特征相对于线性系统发生了根本性的变化。在这种情况下不论外势场如何变化，但非线性Schrodinger方程都能给出具有波-粒二象特性的解，它由包络孤子和一个载波组成，有一个具有确定的位置的质心；同时，微观粒子此时也具有一个确定的质量，能量和动量，和它们遵守的质量，能量和动量守恒定律，在外场作用时粒子是稳定的，并满足经典运动方程和遵守哈密顿方程和拉格朗日方程。于是用非线性Schrodinger方程去描述的微观粒子具有一个明显的的局域特性和波-粒二象性， 从而彻底消除了原有量子力学存在近一个世纪的困难和问题。基于这些新的结果我们可建立起完整和系统的非线性量子力学理论体系，推动量子力学的发展。因此这一研究具有重要意义。 In original quantum mechanics the Schrodinger equation is, in essence, a wave equation, wherein the microscopic particles depicted have only a wave feature, and not a corpuscle nature. These descriptors do not agree only with the Broglie relation of wave-corpuscle duality, but also with experimental results and the traditional knowledge of particle concept. Meanwhile, the theory gives only some approximate solutions. Thus a series of contradictory representations and problems occur in quantum mechanics, which have re-sulted in durative disputations focused on the area of physics and have not led to any united conclusions until now. The only way to solve these problems and difficulties is to develop the quantum mechanics. We inves-tigate in detail wave-corpuscle duality of microscopic particles described by a nonlinear Schrodinger equa-tion in nonlinear quantum systems. Concretely speaking, we here study the properties of the solution of the nonlinear Schrodinger equation, the stability of microscopic particles, invariance 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, and so on. Studied results show that the solution of the nonlinear Schrodinger equation depicting microscopic particles is a soliton and have a wave-corpuscle duality, microscopic particles have always a mass center and possess determinant positions, sizes, mass, mo-mentum, energy and form, their mass, momentum and energy satisfy corresponding conservation laws, their dynamic states can be described by both nonlinear Schrodinger equation and classical Lagrangian and Ham-ilton equations, their motions obey the classical Newton-type law of motion. These properties indicate that the microscopic particles described by a nonlinear Schrodinger equation have a corpuscle nature. However, the solutions of dynamic equation are some solitary waves which are accompanied by a carrier wave to propagate in space-time, and possess certain frequency and wave speed. Thus microscopic particles described by nonlinear quantum mechanics have also wave feature. Thus we can affirm that the microscopic particles depicted by a nonlinear Schrodinger equation have a perfect wave-corpuscle duality, which are in essence different from those in linear quantum mechanics. Based on these results we can establish a new nonlinear quantum mechanics, which can solve these difficulties and problems disputed for about a century in linear quantum mechanics.
Louis de Broglie's celebrated hypothesis transfers a problem of representation of optics to the quantum theories. Let us suppose that the fact that originated the problem in optics is the following, "The images obtained by optical instruments are limited by diffraction. Is the diffraction phenomenon exclusively restricting of the information contained in the image or does it have some physical meaning by itself?" This considered as a problem of measurement of the radiative field does not pose the question of tracing well-defined processes in the sense of the light quantum concept. Despite this the application thereto of quantum formalism makes the essentially inferring statistical nature of measurement forecasting most important. We suggest avoiding the probabilistic conception of measurement by replacing the wave-corpuscle dualistic principle with the duality one. The latter is a basic feature of projective geometry. Referring to it we shall try to include the diffraction in a geometrical model of optics and interpret in that coherent schema the point -plane "wave" dual solution. We show what experimental substantiation the proposed duality has. Lastly, we again discuss the experimental basis of wave-corpuscle dualism.
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.