Non-relativistic Propagators
In non-relativistic quantum mechanics the propagator gives the amplitude for a particle to travel from one spatial point at one time to another spatial point at a later time. It is a Green's function for the Schrödinger equation. This means that if a system has Hamiltonian then the appropriate propagator is a function satisfying
where denotes the Hamiltonian written in terms of the coordinates and denotes the Dirac delta-function.
This can also be written as
where is the unitary time-evolution operator for the system taking states at time to states at time .
Read more about this topic: Propagator