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In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. In Feynman diagrams, which calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the diagram. They also can be viewed as the inverse of the wave operator appropriate to the particle, and are therefore often called ''Green's functions''. ==Non-relativistic propagators== In non-relativistic quantum mechanics the propagator gives the probability amplitude for a particle to travel from one spatial point at one time to another spatial point at a later time. It is the Green's function (fundamental solution) 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, denotes the Dirac delta-function, is the Heaviside step function and is the kernel of the differential operator in question, often referred to as the propagator instead of in this context, and henceforth in this article. This propagator can also be written as : where is the unitary time-evolution operator for the system taking states at time to states at time . The quantum mechanical propagator may also be found by using a path integral, : where the boundary conditions of the path integral include . Here denotes the Lagrangian of the system. The paths that are summed over move only forwards in time. In non-relativistic quantum mechanics, the propagator lets you find the state of a system given an initial state and a time interval. The new state is given by the equation : If only depends on the difference , this is a convolution of the initial state and the propagator. This kernel is the kernel of integral transform. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「propagator」の詳細全文を読む スポンサード リンク
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