受非线性作用的微观粒子的运动特性及其非线性量子力学理论(Ⅰ)

与线性场的情况相比，微观粒子在非线性作用下的运动特性和本性发生很大变化，这说明在线性作用和非线性场中微观粒子的性质是明显不同的．这启示我们必须建立微观粒子在非线性体系或非线性场中运动规律的新理论．为此研究了与线性量子力学描写的微观量子效应迥然不同的宏观量子效应与非线性作用下的孤立子运动的紧密关系．结合现代孤立子理论和超导与超流理论，首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，以及由此理论得出的一些新结论．最后还论证这个理论的正确性和自洽性，理论的运用范围及它的重大意义．

Dynamic Properties of Microscopic Particles Acted by the Non linear Interaction and Non linear Quantum Mechanical Theory

The changes of properties and natures of microscopic paticles to be acted by non linear interactions or in the non lineaar fields are studied,as compared with one described by linear quantum mechanics.The results studied show that the inherent natures of microscopic particles in the non linear fields are completely different from one in linear fields,in the fore an elementary distinction is that the microscopic particles have evidently localized feature,its position and momentum can be determinated simaltaneously,and their motion obeys the classical law,but they have also wave corpuscle double properties.These results obtained necessitate us to establish,of necessity,a new theory of motion of microscopic particals in the non linear fields.Thus the essences and properties of macroscopic quantum effects are studied again,which are obviously different from microscopic quanturm effects described by linear quantum mechanics,and, its relationship with non linear interaction and soliton motion is studied,too.Combined with modern Soliton theory and superconductivity and superfliedity theories,first of all,basic principles and theory of non linear quantum mechanics are introduced,namely,the state of particle in non linear quantum mechanics is described by a wave function concerning the non linear feature;the wave function satisfies generalizing non linear Schrodinger equations in non relativity case or non linear Klein Gordon equations in relativity case.Based on the principles and theory,the theoretical systems of non linear quantum mechanics are established integally and completely and a lot of new results are obtained.Finally the validity and self consistency and application regions of the non linear quantum mechanics are proved. This theory has advanced the development of quantum mechamics from linear region to non linear region,which could solve the serious difficulties and problems of the linear quantum mechanics.And this is a great development and progress of physics.