deletions | additions       diff --git a/section_Abstract_A_200_word__.tex b/section_Abstract_A_200_word__.tex  index db5fb61..782831b 100644  --- a/section_Abstract_A_200_word__.tex  +++ b/section_Abstract_A_200_word__.tex 
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\section{Project Summary}  %A project summary not exceeding 200 words, explaining the work and its significance to laypeople  \section{Proposed Research}  \subsection{Introduction}  %A detailed description of the proposed research, not to exceed 15 single-spaced 11-point pages, including a short statement of how the application fits into the applicant's present research program, and a description of how the results might be communicated to the wider scientific community and general public  \subsection{The precise meaning of time in quantum mechanics} 
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|\Psi_{s-a}(t_u) \rangle = \left[ \mathcal{T}Exp\left[ \int_{0}^{t_u} \left[ \hat{H}_{s} + V(\hat{H}_s, \hat{t}_s, t_a, t_{u}') \right] \right] |\psi_{s}(t_u = 0, t_{a}) \rangle \right] \otimes |\tilde{t}_a \rangle = |\psi_{s}(t_u, \tilde{t}_a- t_u) \rangle \otimes |\tilde{t}_a \rangle  \end{equation}  \subsection{The Born-Oppenheimer approximation for clocks}  \subsection{Implications of the Born-Oppenheimer approximation for chemical ``events"}  \section{References}