Analytical Methods in Classical and Wave Mechanics

R. Faure

Zhuangqi Cao, Cheng Yin

Advances in One-Dimensional Wave Mechanics provides a comprehensive description of the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Utilizing a deeper understanding of the wave nature of matter, this book introduces the concept of the scattered sub-waves and a series of new analytical results using the Analytical Transfer Matrix (ATM) method. This work will be useful for graduate students majoring in physics, mainly in basic quantum theory, as well as for academic researchers exploring electromagnetism, particle physics, and wave mechanics and for experts in the field of optical waveguide and integrated optics. Prof. Zhuangqi Cao is a Professor of Physics at Shanghai Jiao Tong University, China. Dr. Cheng Yin is a teacher at Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, China.

Runsheng Tu

In reality, micro objects and macro objects coexist harmoniously, and each macro object depends on micro particles to exist (macro is a collection of micro objects, indicating that they have a very extensive relationship and are symbiotic). However, classical mechanics and quantum mechanics have long been regarded as binary oppositions. This is a serious disconnect between theory and phenomena, requiring the establishment of new theories and methods that are compatible between quantum and classical. Prior to this, many reasons and methods for combining quantum theory with classical theory have been found (providing numerous computational examples). The wave mechanics equations of classical mechanics laws have been written. The technical method used is still the conversion rule of the Hermitian operator in the fundamental postulates of quantum mechanics. There are no new assumptions. The key is to use the relationship between force and energy in the planetary model to obtain wave mechanics equations that include force, Newton's second law, and the law of conservation of momentum. Thus, quantum mechanics, which is compatible with classical mechanics, truly becomes a form of 'mechanics'. This kind of mechanics is generalized wave mechanics. Quantum and classical are coordinated and compatible, resulting in no clear boundary between quantum and classical. It will seriously affect the credibility of quantum decoherence and wave function collapse.

R. Faure

N. F. Mott, Ian Naismith Sneddon

Zhao Kai-hua

The tortuous path getting to the founding of quantum mechanics in 1925—1926 is reviewed,stressing on the historical heritage from the classical analytical mechanics and the physical ideas full of genius expressed on the way.