quantum mechanics
The analogy between quantum mechanics and probability is very strong, so that there are many mathematical links between them. In a statistical system in discrete time, t=1,2,3, described by a transition matrix for one time step 





K

m
→
n





{\displaystyle \scriptstyle K_{m\rightarrow n}}

, the probability to go between two points after a finite number of time steps can be represented as a sum over all paths of the probability of taking each path:
