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Kinematic theory and dynamical theory of x-ray (or electron) diffraction. Why such names are given to scattering theories ? Does it have any connection to Kinematics (of Galileo) and Dynamics (of Newton) of general physics?

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Kinematics doesn't really have much to do with Galileo anymore, and dynamics doesn't necessarily involve Newton. Instead, those terms are roughly defined as the following:

  • Kinematics is the process of understanding how things move. It involves determining the trajectory of objects without necessarily trying to completely understand the factors that influence that motion (and, in fact, is often deliberately agnostic of the details of forces involved, for example in collisions, where you only care about overall momentum transfer).

  • Dynamics is the process of understanding why things move. It involves determining the forces and other factors that affect an object's motion, without necessarily trying to completely calculate the full trajectory of an object (and, in fact, is often deliberately agnostic of some details of the object's trajectory, for example when path-independent potentials are used).

A kinematical theory of X-ray diffraction will often "integrate out" the details of the forces involved, with the objective of giving you the details of the observed diffraction pattern. In contrast, a dynamical theory of X-ray diffraction will focus on the nature of the specific interactions involved in X-ray diffraction, without necessarily giving you a detailed complete picture of the diffraction pattern on its own.

As you can see, both are necessary in order to understand a physical process, and the line between them is blurrier than you think. Most physical theories have both kinematic and dynamic components.

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