# Time-dependent observables

# Time-dependent observables

This chapter gives an overview of the observables that are of interest in time-dependent density-functional theory, and how to calculate them. Two types of observables are distinguished: explicit and implicit density functionals. Explicit density functionals are, for instance, the density itself, the total particle number, or moments of the density. The total particle number can be defined in a finite volume, which allows one to study ionization processes of atoms and molecules. Moments of the time-dependent density, such as the dipole moment, are important for calculating spectral properties. Examples for implicit density functionals are the probabilities for discrete ionized states, kinetic photoelectron spectra, or state-to-state transition probabilities. These observables can often be approximately expressed as functionals of the Kohn-Sham orbitals. In the last section, the meaning of the time-dependent energy is discussed.

*Keywords:*
time-dependent density, electron localization function, particle number, dipole moment, spectral properties, kinetic photoelectron spectra, time-dependent energy

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