Use of the Wigner representation in scattering problems. Final report
The basic equations of quantum scattering were translated into the Wigner representation: quantum mechanics was put into the form of a stochastic process in phase space, with real-valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed, and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two-body problem. Simple expressions for single- and double-scattering contributions to total and differential cross sections as well as for all necessary shadow corrections are obtained. (auth)
- Research Organization:
- College of William and Mary, Williamsburg, Va. (USA). Dept. of Physics
- OSTI ID:
- 7238152
- Report Number(s):
- N-75-31847; NASA-CR-132737
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUND STATE
CORRECTIONS
CROSS SECTIONS
DIFFERENTIAL CROSS SECTIONS
DISTRIBUTION
MANY-BODY PROBLEM
MECHANICS
MONTE CARLO METHOD
MULTIPLE SCATTERING
PROBABILITY
PROPAGATOR
QUANTUM MECHANICS
SCATTERING
SERIES EXPANSION
STOCHASTIC PROCESSES
TOTAL CROSS SECTIONS
TWO-BODY PROBLEM
WIGNER THEORY