Space-Time Properties of a Scattering Interaction

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Abstract
The scattering of a particle wave packet by a static potential of finite range is considered. In such an interaction, the incident packet enters the potential region, is scattered, and departs, changed in a way which depends on the nature and strength of the interaction. Intuitively there is a region of space and an interval of time in which the interaction occurs. With the aid of the Schrödinger equation, this situation is discussed, and a function is derived which can be interpreted as describing the distribution of the interaction in space and time. The properties of the function are investigated, and arguments are given which support this interpretation. With the distribution, the space-time properties of the interaction are explored. Finally, it it is suggested that the distribution function, appropriately extended, may be a useful tool in studying other aspects of particle interactions.

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