Editing Path integral formulation (section)

=== Coulomb potential ===
Feynman's time-sliced approximation does not, however, exist for the most important quantum-mechanical path integrals of atoms, due to the singularity of the [[Coulomb potential]] {{math|{{sfrac|''e''<sup>2</sup>|''r''}}}} at the origin. Only after replacing the time {{mvar|t}} by another path-dependent pseudo-time parameter
: <math>s = \int \frac{dt}{r(t)}</math>
the singularity is removed and a time-sliced approximation exists, which is exactly integrable, since it can be made harmonic by a simple coordinate transformation, as discovered in 1979 by [[İsmail Hakkı Duru]] and [[Hagen Kleinert]].<ref>{{harvnb|Duru|Kleinert|1979|loc=Chapter 13.}}</ref> The combination of a path-dependent time transformation and a coordinate transformation is an important tool to solve many path integrals and is called generically the [[Duru–Kleinert transformation]].