text: The natural time scale of electron motion in atoms, molecules, and solids is the attosecond (1 as= 10 s). This fact is a direct consequence of quantum mechanics.
  Indeed, for simplicity, consider a quantum particle in superposition between ground-level, of energy , and the first excited level, of energy :
  with  and  chosen as the square roots of the quantum probability of observing the particle in the corresponding state.
  are the time-dependent ground  and excited state  respectively, with  the reduced Planck constant.
  The expectation value of a generic hermitian and symmetric operator, , can be written as , as a consequence the time evolution of this observable is:
  While the first two terms do not depend on time, the third, instead, does. This creates a dynamic for the observable  with a characteristic time, , given by .
  As a consequence, for energy levels in the range of  10 eV, which is the typical electronic energy range in matter, the characteristic time of the dynamics of any associated physical observable is approximately 400 as.
  To measure the time evolution of , one needs to use a controlled tool, or a process, with an even shorter time-duration that can interact with that dynamic.
  This is the reason why attosecond light pulses are used to disclose the physics of ultra-fast phenomena in the few-femtosecond and attosecond time-domain.