since 2006 Help Sitemap 

< Forum >  
< Products >  
< Quantum History Theory >  
< Uda Equation >  
A functional Φ representing an entangled quantum history obeys the new grammar version of Schrödinger equation: where α is a new physical constant with the dimension of (time)^{1} introduced by Yuichi Uda and χ(□ε) is a function defined as ∀t∈R; [χ(□ε)](t) = χ(tε). This equation describes the physical law for a particle with mass m in onedimensional space. V is a function representing a potential energy. I named this equation Uda equation.  I found the Uda equation by the following schematic deduction which is an application of the correspondence principle. Φ[χ] = Π_{k}φ(χ(kε), kε) [M_{new}(Φ) = M_{old}(φ)] i (1/ε){Φ[χ(□ε)]  Φ[χ]} = (1/ε){Π_{k}φ(χ(kεε), kε)  Π_{k}φ(χ(kε), kε)} = (1/ε){Π_{k}φ(χ((k1)ε), kε)  Π_{k}φ(χ(kε), kε)} = (1/ε){Π_{s}φ(χ(sε), (s + 1)ε)  Π_{k}φ(χ(kε), kε)} (s=k1) = (1/ε){Π_{s}φ(χ(sε), sε+ε)  Π_{s}φ(χ(sε), sε)} = Σ_{k}[Π_{s≠k}φ(χ(sε), sε)](∂/∂t)φ(χ(kε), t)_{t=kε} (product rule) = (i = (i = (i → (i ∴ (i By setting ε for 1/α in the above result, we see the Uda equation as a new equation.  This article is a rewrite of the article 'New Grammar Version of Schrödinger Equation' in the following page. Former half@Theory of Quantum History Entangled in Timelike Direction@Products of Grammatical Physics@Grammatical Physics@Forum@Vintage(20082014) The content of this article was presented by me at APS+JPS 2006 Autumn Meeting.  The Uda equation was first thought out in the following articles written in the Japanese language. メッセージ19, 20 @ 1327 @ 時間の量子化 @ 中心問題解決案 @ 文法レベルでの自然 @ Japanese @ Vintage(20052008) These were written on 2005/06/03. 

Author Yuichi Uda, Write start at 2015/05/21/20:52JST, Last edit at 2016/04/05/20:16JST  






