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%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  The wave function of a quantum system describes the probability amplitude for different events to occur at points in space-time. However, the traditional formulation of quantum theory treats space and time on a completely different footing. In non-relativistic quantum mechanics, and chemistry in particular, it is often taken for granted that time is a continuous parameter and not a dynamical variable. If we think of space on the other hand, we know that position is treated as a dynamical variable represented by an operator.  The unequal treatment of space and time in quantum mechanics has many ramifications, particularly when we begin to ask questions about when and where a particular event occurs. The implications of this have been explored extensively in the quantum gravity literature and in fields related to the fundamentals of quantum mechanics. However, the unequal treatment of space and time in quantum chemistry and chemical dynamics has hardly been explored.For instance, the formation of a chemical bond or photodissociation of a molecule can be regarded as a "chemical event" and it is natural to ask not only where this even occurs, but also when.  I propose a research program that will explore the meaning of time in chemical systems. We will explore questions such as: What is a chemical event? How can we define a clock to measure when a chemical event occurs? What are the conditions under which it is valid to treat time as a parameter and not a dynamical variable? 
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\subsection{I. Time Operators in Chemistry and the Meaning of "Chemical Events"}  Time-dependent processes in chemistry are ubiquitous. Chemical reactions occur as molecules collide with one another, exchanging kinetic and potential energy as chemical bonds are formed and broken. Similarly, in photochemical processes photons are absorbed and emitted as energy is channeled into different degrees of freedom (electronic, rotational vibrational). The usual starting Chemical systems such For instance, the formation of a chemical bond or photodissociation of a molecule can be regarded  as atoms, molecules a "chemical event"  and solids are described by it is natural to ask not only where this even occurs, but also when.  %Discuss conditions under which time can be treated as a parameter in chemical systems. What it means for an event to occur in chemistry.