SIMPLIFIED DERIVATION OF THE BINARY COLLISION EXPANSION AND ITS CONNECTION WITH THE SCATTERING OPERATOR EXPANSION

Journal Article · Sun Jun 15 04:00:00 EDT 1958 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.110.1232· OSTI ID:4330529

Siegert, A J.F.; Teramoto, E

The binary collision expansion for the density matrix of a system of N particles with pair interaction was derived by Huang, Lee, and Yang by expansion in the interaction and subsequent summation over terms represented by certain classes of diagrams. A simpler derivation has been obtained by the use of the N(N--1)/2 integral equations which relate the density matrix of the system to the density matrices of systems in which one pair of particles interacts. Successive substitation of the integral equations into each other yields an expansion which by a trivial additional step becomes the binary collision expansion. Our derivation shows also that the binary collision expansion is the Laplace inverse of the coordinate representation of the expansion in terms of scattering operators. (auth)

• Research Organization: Northwestern Univ., Evanston, Ill.
• NSA Number: NSA-12-014378
• OSTI ID: 4330529
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 110; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

COLLISIONS
DENSITY MATRIX
DIAGRAMS
DIFFERENTIAL EQUATIONS
INTERACTIONS
MANY BODY PROBLEM
MATHEMATICS
MATRICES
PHYSICS
QUANTUM MECHANICS
SCATTERING