Lippmann-Schwinger equation in a soluble three-body model: Surface integrals at infinity

Journal Article · Sun Feb 01 00:00:00 EST 1987 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.35.415· OSTI ID:6768714

Gerjuoy, E; Adhikari, S K

At real energies E, the derivation of the Lippmann-Schwinger integral equation from the Schroedinger equation involves various surface integrals at infinity in configuration space. Plausible assumptions about the values of these surface integrals made originally by Gerjuoy imply that the many-particle (n>2) Lippmann-Schwinger equation generally has nonunique solutions. This paper evaluates these surface integrals in the same one-dimensional three-body model (of McGuire) employed recently to demonstrate the nonuniqueness explicitly. The computed values of the surface integrals agree precisely with Gerjuoy's hypotheses. These results further confirm the conclusion that the many-particle Lippmann-Schwinger equation has nonunique solutions in actual three-dimensional collisions, and support the belief that the aforesaid derivation of the real energy Lippmann-Schwinger equation is mathematically sound.

• Research Organization: Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
• OSTI ID: 6768714
• Journal Information: Phys. Rev. C; (United States), Vol. 35:2
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
THREE-BODY PROBLEM
LIPPMANN-SCHWINGER EQUATION
GREEN FUNCTION
ONE-DIMENSIONAL CALCULATIONS
SCATTERING
SCHROEDINGER EQUATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INTEGRAL EQUATIONS
MANY-BODY PROBLEM
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS
653003* - Nuclear Theory- Nuclear Reactions & Scattering