Relation between classical and quantum mechanics

Vladimir K. Ignatovich

Uncertainty relations are shown to have nothing specific for quantum mechanics, being the general property valid for arbitrary function. A wave function of a particle having precisely defined position and momentum in QM simultaneously is demonstrated. Interference on two slits in a screen is shown to exist in classical mechanics. A nonlinear classical system of equations replacing QM Schrödinger equation is suggested. This approach is shown to have nothing in common with Bohmian mechanics.

Enrico G. Beltrametti, Slawomir Bugajski

Wenwen LYU, Feng Wang

This paper introduces the development of the principle of relativity from Galileo's principle of relativity to special relativity and then to general relativity. Inspired by this, we explored the transformation form of quantum mechanics to meet Galileo's principle of relativity. Firstly, from the point that unitary transformation can keep the physical laws of quantum mechanics unchanged, we correspond the momentum translation unitary transformation in quantum mechanics to the Galileo transformation in classical mechanics, and reveal that the transformation form of quantum mechanics that meets the Galileo principle of relativity can be realized through the momentum translation unitary transformation. This inquiry is conducive to students' in-depth thinking about the corresponding relationship between quantum mechanics and classical physics, can help beginners reduce the conflict between quantum physics and classical physics, and help students build a bridge from classical to quantum thinking.

Skender, Ahmetaj, Kabashi +3 more

Zhu Hengjiang

Quantum mechanics and classical mechanics are closely related to each other.The Hamilton-Jacobi Equation of classical mechanics plays an important role in the extension of Schrdinger equation,and it is also a way to extend Schrdinger equation in the teaching of quantum mechanics.Besides,the Hamilton-Jacobi Equation under the theory of relativity can extend Klein-Gordon equation of quantum mechanics of special relativity.Considering and analyzing the differences betweeen Klein-Gordon equation and Dirac Equation further,this paper linearized the Hamilton-Jacobi Equation under the theory of relativity,and extended Dirac Equation which was more important than quantum mechanics of special relativity.It made the route by which Hamilton-Jacobi Equation,as the classical mechanics,goes to quantum mechanics more extensive,and this study further explored the corresponding relationship between classical mechanics and quantum mechanics.

Philip Yu