Nonlinear wave mechanics

Louis de Broglie

Philip M. Barnes

Fayçal Hammad

Zhiqiang Huang

This paper get a general survey of advances in Wave Mechanics.The development of Wave Mechanics goes back to ancient times.The principle of least action is the source of Wave Mechanics,so it is the mother of several principles.Erwin Schrdinger was the greatest contribution scientist of Wave Mechanics,secondary was Louis de Broglie.The Schrdinger equation not only can treat the movement of microscopic particles,but also can analysed some of the macroscopic scientific problems.There's no time for Schrdinger to study the non-linear Schrdinger equation(NLS),but de Broglie devoted oneself to the study of nonlinear Wave Mechanics,and established contact with the solitary waves.At present,the most research works involve the nonlinear differential equations in mathematics,but ignore the physical meaning.In the sciences of waves,the study of electro-magnetic waves are important field,many problems demand clarification.From the Wave Mechanics point of view,we must integrate the classic electro-magnetic wave equation with the Quantum Mechanics wave eqution,the isolated discussion age of classic fields and waves was extremely early ended.

Boris V. Alexeev

Shortcomings of the Boltzmann physical kinetics and the Schrödinger wave mechanics are considered. From the position of nonlocal physics, the Schrödinger equation is a local equation; this fact leads to the great shortcomings of the linear Schrödinger wave mechanics. Nonlocal nonlinear quantum mechanics is considered using the wave function terminology.

Pierre Meystre