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Encouraged by the success of Exact Solution of Uda Equation (2) @ Quantum History Theory @ Products, I began to hope that any classical motion appears asymptotically generally as a delta function factor in a solution. In this page, I try to write such a solution for harmonic oscillator problem. x(t) = A sin(ωt  B), x(a) = A sin(ωa  B), x(b) = A sin(ωb  B). ωa  B = sin^{1}[x(a)/A], ωb  B = sin^{1}[x(b)/A], ω(b  a) = sin^{1}[x(b)/A]  sin^{1}[x(a)/A], sin[ω(b  a)] = [x(b)/A]cos{sin^{1}[x(a)/A]}  cos{sin^{1}[x(b)/A]}[x(a)/A] = ±[x(b)/A]√{1  [x(a)/A]^{2}} ± [x(a)/A]√{1  [x(b)/A]^{2}} = ±[ [x(b)/A]√{1  [x(a)/A]^{2}} + [x(a)/A]√{1  [x(b)/A]^{2}} ] or ±[ [x(b)/A]√{1  [x(a)/A]^{2}}  [x(a)/A]√{1  [x(b)/A]^{2}} ] A^{2}sin[ω(b  a)] = ±{x(b)√[A^{2}  x(a)^{2}] + x(a)√[A^{2}  x(b)^{2}]} or ±{x(b)√[A^{2}  x(a)^{2}]  x(a)√[A^{2}  x(b)^{2}]}. How about putting as follows? Φ[χ] = δ( lim_{a→∞}lim_{b→+∞}{χ(b)√[A^{2}  χ(a)^{2}] + χ(a)√[A^{2}  χ(b)^{2}]  A^{2}sin[ω(b  a)]} )F[χ]. For the present, I decided to stop going on this way more because of too less hope.(2019/10/14) 

Author Yuichi Uda, Write start at 2019/10/13/15:10JST, Last edit at 2019/10/14/14:45JST  






