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\begin{document}

\title{\begin{CJK}{UTF8}{gbsn}確率的収束\end{CJK}\selectlanguage{english}(2)\selectlanguage{english}}



\author[1]{quantumtimemeasure}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 08, 2024}


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\begin{CJK}{UTF8}{gbsn}測定\end{CJK}\selectlanguage{english}suruto\begin{CJK}{UTF8}{gbsn}波束\end{CJK}\selectlanguage{english}ga\begin{CJK}{UTF8}{gbsn}収束\end{CJK}\selectlanguage{english}surutoiukopenhagen\begin{CJK}{UTF8}{gbsn}解釈\end{CJK}\selectlanguage{english}ha\begin{CJK}{UTF8}{gbsn}、測定\end{CJK}\selectlanguage{english}ga\begin{CJK}{UTF8}{gbsn}特別\end{CJK}\selectlanguage{english}namonodeari\begin{CJK}{UTF8}{gbsn}気\end{CJK}\selectlanguage{english}ni\begin{CJK}{UTF8}{gbsn}入\end{CJK}\selectlanguage{english}ranainode\begin{CJK}{UTF8}{gbsn}、測定\end{CJK}\selectlanguage{english}siyougasimaiga\begin{CJK}{UTF8}{gbsn}、任意\end{CJK}\selectlanguage{english}no\begin{CJK}{UTF8}{gbsn}状態\end{CJK}\selectlanguage{english}$|\alpha \rangle \in \mathscr{H}$ha\begin{CJK}{UTF8}{gbsn}、微小時間間隔\end{CJK}\selectlanguage{english}$dt$nioite\begin{CJK}{UTF8}{gbsn}、任意\end{CJK}\selectlanguage{english}no\begin{CJK}{UTF8}{gbsn}正規直行基底\end{CJK}\selectlanguage{english}$\{ |q_i\rangle \}$no\begin{CJK}{UTF8}{gbsn}一\end{CJK}\selectlanguage{english}tu$\exp(i \cdot  \arg(\langle q_i|\alpha\rangle))|q_i\rangle \in \mathscr{H}$ni\begin{CJK}{UTF8}{gbsn}、確率 \end{CJK}\selectlanguage{english}$| \langle q_i |\alpha \rangle |\rho  dt$de\begin{CJK}{UTF8}{gbsn}収束\end{CJK}\selectlanguage{english}suruto\begin{CJK}{UTF8}{gbsn}仮定\end{CJK}\selectlanguage{english}suru\begin{CJK}{UTF8}{gbsn}。\end{CJK}\selectlanguage{english}$t$ga\begin{CJK}{UTF8}{gbsn}十分小\end{CJK}\selectlanguage{english}saitosuruto\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$( \rho dt)^{2}$ha\begin{CJK}{UTF8}{gbsn}無視\end{CJK}\selectlanguage{english}dekirunode\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}1\begin{CJK}{UTF8}{gbsn}回収束\end{CJK}\selectlanguage{english}suru\begin{CJK}{UTF8}{gbsn}場合\end{CJK}\selectlanguage{english}nomiwo\begin{CJK}{UTF8}{gbsn}考\end{CJK}\selectlanguage{english}ereba\begin{CJK}{UTF8}{gbsn}十分\end{CJK}\selectlanguage{english}deari\begin{CJK}{UTF8}{gbsn}、
\end{CJK}\selectlanguage{english}$$
\hat\langle \alpha ',t'|\alpha ,0\hat\rangle =\left( 1-\rho \int ^{ t'}_{0} dt\sum_i  |\langle q_i,t|\alpha ,0\rangle |\right) \langle \alpha ', t'|\alpha ,0\rangle +\rho \int ^{ t'}_{0} dt\sum_i \mathrm{e}^{i \cdot  \arg(\langle q_i|\alpha\rangle)} \langle \alpha ',t'|q_i,t\rangle |\langle q_i,t|\alpha ,0\rangle |
$$
tonaru\begin{CJK}{UTF8}{gbsn}。\end{CJK}\selectlanguage{english}kokode\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$\hat\langle ,|,\hat\rangle$ha\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}kopenhagen\begin{CJK}{UTF8}{gbsn}解釈\end{CJK}\selectlanguage{english}to\begin{CJK}{UTF8}{gbsn}異\end{CJK}\selectlanguage{english}nari\begin{CJK}{UTF8}{gbsn}、確率的\end{CJK}\selectlanguage{english}ni\begin{CJK}{UTF8}{gbsn}状態\end{CJK}\selectlanguage{english}ha\begin{CJK}{UTF8}{gbsn}収束\end{CJK}\selectlanguage{english}suruto\begin{CJK}{UTF8}{gbsn}仮定\end{CJK}\selectlanguage{english}sita\begin{CJK}{UTF8}{gbsn}場合\end{CJK}\selectlanguage{english}no\begin{CJK}{UTF8}{gbsn}遷移確率振幅、\end{CJK}\selectlanguage{english}$\langle , | ,\rangle$ha\begin{CJK}{UTF8}{gbsn}一般的\end{CJK}\selectlanguage{english}nakopenhagen\begin{CJK}{UTF8}{gbsn}解釈\end{CJK}\selectlanguage{english}nomotodeno\begin{CJK}{UTF8}{gbsn}遷移確率振幅\end{CJK}\selectlanguage{english}dearu\begin{CJK}{UTF8}{gbsn}。
\end{CJK}\selectlanguage{english}$$|\langle q,t|\alpha ,0\rangle |=\langle q,t|\alpha ,0\rangle \mathrm{e}^{-i \cdot  \arg(\langle q,t|\alpha ,0\rangle)}$$
dearunode\begin{CJK}{UTF8}{gbsn}、【以下間違\end{CJK}\selectlanguage{english}i\begin{CJK}{UTF8}{gbsn}】
\end{CJK}\selectlanguage{english}$$
\hat\langle \alpha ',t'|\alpha ,0\hat\rangle =( 1-\rho  t') \langle \alpha ', t'|\alpha ,0\rangle +\rho \int ^{ t'}_{0} dt\sum_i dq\langle \alpha ', t'|q_i,t\rangle \langle q_i,t|\alpha ,0\rangle 
$$
tonaru\begin{CJK}{UTF8}{gbsn}。
\end{CJK}\selectlanguage{english}tokoroga\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$|q_i,t\rangle \in \mathscr{H}$ha\begin{CJK}{UTF8}{gbsn}正規直交基底\end{CJK}\selectlanguage{english}nanode\begin{CJK}{UTF8}{gbsn}、
\end{CJK}\selectlanguage{english}$$
\int ^{ t'}_{0} dt\sum_i \langle \alpha ', t|q_i,t\rangle \langle q_i,t|\alpha ,0\rangle = \int ^{ t'}_{0} dt \langle \alpha ', t'|\alpha ,0\rangle =  t' \langle \alpha ', t'|\alpha ,0\rangle
$$
deari\begin{CJK}{UTF8}{gbsn}、
\end{CJK}\selectlanguage{english}$$
\hat\langle \alpha ', t'|\alpha ,0\hat\rangle =\langle \alpha ', t'|\alpha ,0\rangle 
$$
tonaru\begin{CJK}{UTF8}{gbsn}。\end{CJK}\selectlanguage{english}sitagatute\begin{CJK}{UTF8}{gbsn}、確率的\end{CJK}\selectlanguage{english}ni\begin{CJK}{UTF8}{gbsn}収束\end{CJK}\selectlanguage{english}ga\begin{CJK}{UTF8}{gbsn}発生\end{CJK}\selectlanguage{english}surutositemo\begin{CJK}{UTF8}{gbsn}、遷移確率振幅\end{CJK}\selectlanguage{english}ha\begin{CJK}{UTF8}{gbsn}変\end{CJK}\selectlanguage{english}waranai\begin{CJK}{UTF8}{gbsn}。




\end{CJK}\selectlanguage{english}$|q_n\rangle$wohamirutonianno\begin{CJK}{UTF8}{gbsn}固有状態、\end{CJK}\selectlanguage{english}sunawati\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$H|q_n\rangle = E_n|q_n\rangle$tosite\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$|\alpha \rangle = c_1|q_1\rangle + c_2|q_2\rangle$no\begin{CJK}{UTF8}{gbsn}場合\end{CJK}\selectlanguage{english}wo\begin{CJK}{UTF8}{gbsn}考\end{CJK}\selectlanguage{english}eyou\begin{CJK}{UTF8}{gbsn}。時間\end{CJK}\selectlanguage{english}ga\begin{CJK}{UTF8}{gbsn}十分経\end{CJK}\selectlanguage{english}teba\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$|\alpha \rangle $ha\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$\frac{|c_1|}{|c_1|+|c_2|}$no\begin{CJK}{UTF8}{gbsn}確率\end{CJK}\selectlanguage{english}de$|q_1\rangle $no\begin{CJK}{UTF8}{gbsn}状態\end{CJK}\selectlanguage{english}ninatuteiruto\begin{CJK}{UTF8}{gbsn}考\end{CJK}\selectlanguage{english}erareru\begin{CJK}{UTF8}{gbsn}。一方、\end{CJK}\selectlanguage{english}kopenhagen\begin{CJK}{UTF8}{gbsn}解釈\end{CJK}\selectlanguage{english}deha\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}$\frac{|c_1|^2}{|c_1|^2+|c_2|^2}$no\begin{CJK}{UTF8}{gbsn}確率\end{CJK}\selectlanguage{english}de$|q_1\rangle $no\begin{CJK}{UTF8}{gbsn}状態\end{CJK}\selectlanguage{english}ninatuteiruto\begin{CJK}{UTF8}{gbsn}考\end{CJK}\selectlanguage{english}erareru\begin{CJK}{UTF8}{gbsn}。

\end{CJK}\selectlanguage{english}\selectlanguage{english}
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