Features and states of microscopic particles in nonlinear quantum-mechanics systems

Abstract

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. 02 .60.Cb, As is known, the quantum mechanics established by several great scientists such as Bohr, Born, Schrödinger and Heisenberg, etc., in the early 1900s [1 − 6] is the science describing the properties and rules of motion of microscopic particles (MIP). It is a foundation of modern science, in which the state of microscopic particles is described by the Schrödinger equation: PACS numberswhere 2 ∇ 2 /2m is the kinetic energy operator, V (r, t) is

The Changes of States and Properties of Microscopic Particles Under Influences of Different External Potential Fields

“…Our investigations [13][14][15][16][17][18][19][20][21][22] show that when the motions of the microscopic particles and background field (nucleon) in solid and organic molecules (atoms) and the interaction between them are simultaneously considered, nonlinear interaction, b|φ 2 |φ, occurs in the systems. The nonlinear interaction can be produced through self-interaction and self-condensation among the particles or self-focusing effect of medium and self-trapping mechanism of background field, and so on.…”

“…The nonlinear interaction can be produced through self-interaction and self-condensation among the particles or self-focusing effect of medium and self-trapping mechanism of background field, and so on. [13][14][15][16][17][18][19][20][21][22][23] In this case the natures and states of the microscopic particles are no longer depicted by Eq. (1), but by the following nonlinear Schrödinger equation:…”

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA

“…Nonlinear mathematics and physics are well known as rapidly developing areas of natural science with numerous interesting applications, such as deoxyribonucleic acid (DNA) science [1][2][3][4][5][6][7][8][9][10]. DNA plays a vital role in all living organisms since it is the key molecule responsible for duplication, storage, and realization of genetic information [11].…”

The Properties of the Solutions of Nonlinear Schrödinger Equation with Center Potential

“…Meanwhile, Pang used the nonlinear Schrödinger equation in Eq. (3) to depict the states and motions of microscopic particles in nonlinear quantum mechanics [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], where ( , ) r t f  is a wave function of state of microscopic particle, m is the mass of the particle, 2 2 / 2m ∇  is its kinetic energy operator, ( ) , V r t  is the externally applied potential, which is related to the positions of particles or a constant, r  is its position,…”

“…This equation has, in general, a soliton solution [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. This means that the microscopic particles move in a soliton states in microscopic systems.…”