Editing Probability amplitude (section)

==Amplitudes in operators==
The concept of amplitudes is also used in the context of [[scattering theory]], notably in the form of [[S-matrix|S-matrices]]. Whereas moduli of vector components squared, for a given vector, give a fixed probability distribution, moduli of [[matrix element (physics)|matrix element]]s squared are interpreted as [[transition probabilities]] just as in a random process. Like a finite-dimensional [[unit vector]] specifies a finite probability distribution, a finite-dimensional [[unitary matrix]] specifies transition probabilities between a finite number of states.

The "transitional" interpretation may be applied to {{math|''L''<sup>2</sup>}}s on non-discrete spaces as well.{{clarify|reason= [applied to ..] as opposed to what? On what "non-discrete space"?|date=November 2023}}