# JPS 2007 Spring Meeting

- SourceCodeOf_HumanGenome > Abstracts for the Meetings Held by the Physical Society @ 2009/2/7 11:23
- SourceCodeOf_HumanGenome > JPS 2005 Autumn Meeting @ 2009/2/15 10:42
- SourceCodeOf_HumanGenome > Grammatism @ 2009/2/20 15:45
- SourceCodeOf_HumanGenome > JPS 2006 Spring Meeting @ 2009/4/25 10:17
- SourceCodeOf_HumanGenome > Not 'analyzable' but 'entangled' @ 2009/7/27 9:42
- SourceCodeOf_HumanGenome > APS+JPS 2006 Autumn Meeting @ 2009/7/28 10:01
*»*SourceCodeOf_HumanGenome >*JPS 2007 Spring Meeting*@ 2009/8/4 9:55- SourceCodeOf_HumanGenome > JPS 2008 Spring Meeting @ 2009/9/3 9:17
- SourceCodeOf_HumanGenome > JPS 2008 Autumn Meeting @ 2009/11/13 10:08
- SourceCodeOf_HumanGenome > Errors are in the equations. @ 2010/1/18 10:06
- SourceCodeOf_HumanGenome > JPS 2009 Spring Meeting @ 2010/1/26 9:43
- SourceCodeOf_HumanGenome > JPS 2009 Autumn Meeting @ 2010/5/24 11:15
- SourceCodeOf_HumanGenome > JPS 2010 Spring Meeting @ 2010/9/20 10:26

SourceCodeOf_HumanGenome > JPS 2007 Spring Meeting @ 2009/8/4 9:55 |
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28pSL-11 New grammar version of Schrodinger equation Uda's School / Yuuichi Uda --- About a system with one degree of freedom, I want to find an equation obeyed by Φ in the new grammar, which represents a quantum history whose quantum state at time t is represented by wave function ψ(□,t) by the following functional Φ. Φ[χ]=exp[α∫dt φ(χ(t),t)]; ψ(x,t)= exp φ(x,t)・・・※ As a clue, it seems plausible course to select the equation for Φ as it reduces to the ordinary schrodinger equation for ψ in the special case that ※ holds. Along this course, I tried making the following equation. (ih／2πα) lim (1／ε)(Φ[χ']－Φ[χ]) ε→0 ＝∫dt[(1／2m)(－ih／2πα)^2(δ／δχ(t))^2＋V(χ(t))]Φ[χ], where χ'(t)=χ(t-ε). I have not yet confirmed whether this equation always reduces to Schrodinger equation in the special case ※. Besides, I got some undesirable result when I investigated a solution corresponding to the ground state of a harmonic oscillator. It is the result that Φ[χ]＝exp[α∫dt(－π／h)√(mk)(χ(t))^2] is a solution when V(x)＝kx^2－(h／4πα)δ(0)√(k／m). Adding an arbitrary constant to potential energy does not change what physical system we treat, and so it may not be undesirable, but the appearance of the value of δ-function at zero point might mean failure of the theory in the worst case. In order that V(x)＝kx^2, perhaps we have only to formally select Φ[χ]＝exp[α∫dt[－Et－(π／h)√(mk)(χ(t))^2]], using a real constant E. However, in this case, too, perhaps E includes δ(0), and we should understand that integral ∫dt[－iEt] is not well defined or is zero, and so room for criticism is left. It might be a way for settling these problems that renew χ'(t)＝χ(t－ε). For example, how about using an arbitrary function f such that f(t)＝t if t＜a or t＜b, selecting χ'(t)＝χ(f(t)), and altering the Hamiltonian part after it? In order to avoid being criticized for the point that ψ(x,t) has a dimension of (length)^(-3/2) despite that φ(x,t) is dimensionless, we have only to reselect ψ(x,t)＝βexpφ(x,t) using a dimensionful factor β. --- Last edited at 2010/05/01/15:33JST |

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