Editing Cross section (physics) (section)

=== Relation to the S-matrix ===
If the [[reduced mass]]es and [[Momentum|momenta]] of the colliding system are {{math|''m''<sub>i</sub>}}, {{math|'''p'''<sub>i</sub>}} and {{math|''m''<sub>f</sub>}}, {{math|'''p'''<sub>f</sub>}} before and after the collision respectively, the differential cross section is given by{{clarify|reason=This section is an uncontextualized leap. We have jumped, without announcement, from the Schrödinger PDE for a wave in a potential to the language of QFT for two particles colliding.|date=September 2016}}
: <math>\frac{\mathrm d\sigma}{\mathrm d\Omega} = \left(2\pi\right)^4 m_\text{i} m_\text{f} \frac{p_\text{f}}{p_\text{i}} \bigl|T_{\text{f}\text{i}}\bigr|^2,</math>
where the on-shell {{math|''T''}} matrix is defined by
: <math>S_{\text{f}\text{i}} = \delta_{\text{f}\text{i}} - 2\pi i \delta\left(E_\text{f} - E_\text{i}\right) \delta\left(\mathbf{p}_\text{i} - \mathbf{p}_\text{f}\right) T_{\text{f}\text{i}}</math>
in terms of the [[S-matrix]]. Here {{math|''δ''}} is the [[Dirac delta function]]. The computation of the S-matrix is the main goal of the [[scattering theory]].