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over a certain domain of the Hilbert space spanned by the states $\{ |\psi_n \rangle \}$. Note that eq.~\ref{full_t} is a non-linear eigenvalue problem, as one must find both the operator $\hat{t}$ and the eigenvectors $\{ |\psi_n \rangle \}$. Non-linear eigenvalue problems are common in computational chemistry and many highly efficient numerical algorithms exist. My group has vast computational resources available to accomplish this task. After constructing $t$, we can investigate its spectrum and answer questions about chemical events such as: When does a molecule absorb or emit a phonton? When does the absorbed energy fully dissipate into nuclear vibrational energy? How long does it take for a chemical reaction between two molecules to occur?  The task of constructing a time operator for the full Hamiltonian in eq.~\ref{full_H} will be computationally demanding. Approximate and model Hamiltonians are often used to simply quantum many-body calculations. Each model Hamiltonian gives rise to a corresponding model time operator through the solution to eq.~\ref{full_t}. Another area of research will be to construct and classify time operators for different model Hamiltonians of varying degrees of complexity. For example, in chemistry it is often possible to make approximations to simplify eq.~\ref{full_H}. By invoking the Born-Oppenheimer approximation (BO), one can treat the nuclei classically as well as the electromagnetic field and arrive at the electronic Hamiltonian:  \begin{equation}  \hat{H} = \int d^3 r  \end{equation}  %satisfying canonical commutation relations with the chemical Hamiltonian and not a parameter. I propose to e will construct time operators