The Time-Dependent Picture Terminology

Just as a satisfactory approximation to the exact solution of the time-independent Schrodinger equation for a many-electron molecule must be expressed in a form that belies the apparent simplicity of the spectrum, so too is the exact solution of the time-dependent Schrodinger equation often opaquely complex. For the time-independent problem, insight comes from defining a suitable zero-order model specifying the essential coupling terms (tT1)) and 

When the state of a molecule evolves under the influence of a time-independent H, structure and dynamics are two sides of the same coin. Since the same H appears in the time-independent and time-dependent Schrodinger equations, an Heff-based intuitive picture of the molecular structure generates an intuitive, causal, mechanistic picture of molecular dynamics. 

A dynamical mechanism consists of the following elements (i) creation of a nonstationary state-, (it) departure of the nonstationary state from its initial location in coordinate or state space (Hi) long time evolution, including partial rephasings and decay. 

A dynamical mechanism is specified by answering the classic questions about the time-evolution of an isolated system where does it start, how fast does it leave, what causes it to leave, where does it go next, and why does it go there Answers to all of these questions are obtainable by constructing an appropriate Heff model following the techniques presented in Chapters 1-8. The parameters that define the Heff may equally well be defined by fitting the information contained in a frequency domain (transition frequencies, intensities, and linewidths) or a time domain (arrival times of the wavepacket at a specified location in coordinate or state space, decay rates, transfer rates, and recurrence times and amplitudes) experiment. 

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