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Levinson's theorems in classical scattering

Journal Article · · Phys. Rev., A; (United States)
This paper states and proves Levinson's theorems for the classical scattering of two particles. The derivation is carried out by using time-delay theory. In both classical and quantum mechanics Levinson's theorems are shown to be the consequence of a common principle. This principle is the spectral property of time delay. Consider an arbitrary space region v. In quantum and classical mechanics a time-dependent scattering state traverses v in a definite time. The spectral property states that the sum of transit times for all orbits with total energy epsilon is proportional to the state density in region v. In classical mechanics it is established that this property can be derived from simple features of the time-evolution group.
Research Organization:
Cyclotron Laboratory, Department of Physics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
OSTI ID:
5326897
Journal Information:
Phys. Rev., A; (United States), Journal Name: Phys. Rev., A; (United States) Vol. 22:1; ISSN PLRAA
Country of Publication:
United States
Language:
English

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