N-body quantum scattering theory in two Hilbert spaces. I. The basic equations

Journal Article · Wed Nov 30 23:00:00 EST 1977 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523243· OSTI ID:7076896

Chandler, C; Gibson, A G

Derivations are given for some transition and resolvent operator equations for multichannel quantum scattering with short-range potentials. The basic difference between these and previous equations is that the unknown operators act only on the channel subspaces. This is made possible by utilizing, and extending, the two-Hilbert-space formulation previously given by the authors (in J. Math. Phys. 14, 1328 (1973)). The equations in abstract form are of the Lippmann--Schwinger type, differing only in the appearance of certain injection operators from one Hilbert space to the other. When applied to multichannel quantum scattering, the abstract theory yields a new system of equations for the transition and resolvent operators. Uniqueness of the solution to the equations is proved.

• Research Organization: Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131
• OSTI ID: 7076896
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 18:12; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
EQUATIONS
HILBERT SPACE
INTEGRAL EQUATIONS
LIPPMANN-SCHWINGER EQUATION
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
QUANTUM MECHANICS
SCATTERING
SPACE