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25pZC-1
The new quantum grammar version of Ehrenfest condition
Live lesson culture school / Yuuichi Uda
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The new quantum grammar here is the new grammar proposed by me at JPS 2006 Spring Meeting 27pXA-6.
At JPS 2007 Spring Meeting 28pSL-11, I published a candidate for new grammar version of Shrodinger equation representing the physical law in this new grammar.
However, I am still not quite confident that the equation proposed then is plausible.
Accordingly, this time, I propose a condition which I think to be pretty plausible as a candidate for the condition obeyed by the new grammar version of Schrodinger equation.
I should like to check afterwards if the equation showed by me at JPS 2007 Spring Meeting 28pSL-11 obeys this condition.
The new grammar proposed by me at JPS 2006 Spring Meeting 27pXA-6 represents a quantum history whose quantum state at time t is represented by a wave function ψ(□,t) in the ordinary quantum mechanics by such a functional Φ as
Φ[χ]＝exp[α∫dtφ(χ(t),t)]; ψ(x,t)＝exp φ(x,t),
concerning a system with one degree of freedom.
Accordingly, this time, I propose the new grammar version of Ehrenfest condition as the following equation.
m(d/dt)(d/dt)∫Dχ Φ[χ]*χ(t)Φ[χ]
＝－∫Dχ Φ[χ]*V'(χ(t))Φ[χ] ・・・・・・※
Here, Φ[χ]* is the complex conjugate of Φ[χ], and V' is a function defined as V'(x)≡(d/dx)V(x) using potential energy V.
The measure of the functional integral ∫Dχ is selected to be
∞ ∞
lim Π ∫dx(nε).
ε→+0 n＝－∞ －∞
Condition ※ is pretty plausible because it is very similar to both the expression of Ehrenfest theorem in the existing quantum mechanics and the equation of motion in the classical mechanics.
The new grammar version of the equation probably must be made as the condition ※ is derived from it.
This reason can be used as a pretty powerful guiding principle for finding out the new grammar version of the equation.
Ref. Joint Meeting Of Pacific Region Particle Physics Communities Monday 30 October 2006 International Outreach.
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This article is a rewrite of the following article.
JPS 2008 Spring Meeting@Abstracts for the Meetings Held by the Physical Society@Definition of Grammatical Physics@Grammatical Physics@Forum@Vintage(2008-2014)
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