Two problems in Classical Mechanics

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-I

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-II

The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.

非决定论与经典力学

Indeterminism and classical mechanics

本文结合动力学混沌与物理现象和数学模型的区分，挑战经典力学的决定论观点，并在准现实例子中量化非决定论。

A duality in classical and quantum mechanics: General results

We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In a duality family, once a system is solved, all other potentials are solved by the dual transform. That is, in a duality family, we only need to solve one system.

Comment on "Analyzing collisions in classical mechanics using mass-momentum diagrams" by A. Ogura, arXiv:1809.01768

A change of axes and notation would improve an otherwise excellent teaching diagram.

A classical fermionic system that follows the fundamental rules of Quantum Mechanics

It is feasible to obtain any basic rule of the already known Quantum Mechanics applying the Hamilton-Jacobi formalism to an interacting system of 2 fermionic degrees of freedom. The interaction between those fermionic variables unveils also a primitive spin and zitterbewegung.