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The equation was later extended to quantum scattering theory by several individuals, and came to be known as the Bohr–Peierls–Placzek relation after a 1939 paper. It was first referred to as the "optical theorem" in print in 1955 by Hans Bethe and Frederic de Hoffmann , after it had been known as a "well known theorem of optics" for some time.
The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles ...
The following description follows the canonical way of introducing elementary scattering theory. A steady beam of particles scatters off a spherically symmetric potential V ( r ) {\displaystyle V(r)} , which is short-ranged, so that for large distances r → ∞ {\displaystyle r\to \infty } , the particles behave like free particles.
Rutherford scattering cross-section is strongly peaked around zero degrees, and yet has nonzero values out to 180 degrees. This formula predicted the results that Geiger measured in the coming year. The scattering probability into small angles greatly exceeds the probability in to larger angles, reflecting the tiny nucleus surrounded by empty ...
The Glauber multiple scattering theory [1] [2] is a framework developed by Roy J. Glauber to describe the scattering of particles off composite targets, such as nuclei, in terms of multiple interactions between the probing particle and the individual constituents of the target.
Levinson's theorem is an important theorem of scattering theory. In non-relativistic quantum mechanics, it relates the number of bound states in channels with a definite orbital momentum to the difference in phase of a scattered wave at infinite and zero momenta. It was published by Norman Levinson in 1949.
In physical problems, this differential equation must be solved with the input of an additional set of initial and/or boundary conditions for the specific physical system studied. The Lippmann–Schwinger equation is equivalent to the Schrödinger equation plus the typical boundary conditions for scattering problems.
Given the laws of individual collision events (in the form of absorption coefficients and scattering kernels/phase functions) the problem of linear transport theory is then to determine the result of a large number of random collisions governed by these laws.