Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory

TL;DR

This paper introduces a mechanical wave theory based on wave-particle duality, deriving new operators and nonlinear equations that could enhance understanding of quantum phenomena.

Contribution

It presents a novel approach replacing wave quantities in mechanical equations, leading to new operators and nonlinear equations for quantum theory.

Findings

Derived new physical operators from wave quantities.

Proposed nonlinear equations with potential quantum applications.

Suggested solutions to these nonlinear equations.

Abstract

Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.