When the states and properties of microscopic particles were described by linear SchrÖdinger equation the quantum mechanics had a lot of difficulties, which cause a centenary controversy in physics and have not a determinate conclusions till now. Thus we used a nonlinear SchrÖdinger equation to replace the linear SchrÖdinger equation and to depict and study in detail the states, properties and rules of motion of microscopic particles. Concretely speaking, we here investigated the properties and rules of wave-particle duality of microscopic particles and its stability, the invariances and conservation laws of motion of particles, the classical rule of motion, Hamiltonian principle of particle motion, corresponding Lagrangian and Hamilton equations for the microscopic particle, the mechanism and rules of particle collision in different nonlinear systems, the uncertainty relation of position and momentum of particles, the features of reflection and transmission of the particles at interfaces as well as the eigenvalue and eigenequations of the particles, and so on. The results obtained from these investigations show clearly that the microscopic particles described by the nonlinear SchrÖdinger equation have exactly a wave- particle duality, motions of its centre of mass meet not only classical equation of motion but also the Lagrangian and Hamilton equations, its mass, energy and momentum and angular momentum satisfy corresponding invariances and conservation laws, their collision has the feature of collision of classical particles, the uncertainty of position and momentum of the particles has a minimum, it is a bell-type solitary wave contained envelope and carrier wave, which but differs from not only KdV solitary wave but linear wave, its eigenvalues and eigenequations obey Lax principle and possess plenty of unusual peculiarities. The above natures and properties of the particles are different completely and in essence from those described the linear SchrÖdinger

How to Cite
XIAO-FENG, Pang. The Difficulties of Quantum Mechanics and its Investigations of Development. Global Journal of Science Frontier Research, [S.l.], nov. 2016. ISSN 2249-4626. Available at: <https://journalofscience.org/index.php/GJSFR/article/view/1880>. Date accessed: 23 jan. 2022.