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arXiv:1008.2802

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

Yi‐Fang Chang

Published Aug 17, 2010• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.1008.2802

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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.
First, various dualities are summarized. Next, 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 v and wave length  are replaced on various mechanical equations, and may 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.
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Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of wave-particle duality developed in this paper. Based on the unified theory of wave-particle duality, a straightforward derivation of the Schrödinger equations is presented where previously no such derivation was considered to be possible. A new theory of quantum diffraction is subsequently developed.
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of wave-particle duality developed in this paper. Based on the unified theory of wave-particle duality, a straightforward derivation of the Schrodinger equations is presented where previously no such derivation was considered to be possible. A new theory of quantum diffraction is subsequently developed.
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