Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
29 (1988), S. 155-168
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
An algebraic formulation of the problem of three particles in one dimension is given, where the particles interact with delta function potentials of arbitrary strength and have almost arbitrary mass. An algebraic formulation is taken to mean that the steps implied from formulation to solution involve finite algebra. The canonical example is equal mass particles interacting with equal strength delta function potentials, where the Bethe ansatz holds and the solution involves only sums of products of matrices with elements that are rational functions of a complex variable. When the Bethe ansatz fails the Sommerfeld diffraction ansatz is satisfied if a condition of internal consistency is met. This condition of internal consistency requires the solution to a Riemann–Hilbert functional equation with an algebraic coefficient. The solution to this functional equation is an analytic, but not generally a meromorphic function. It is demonstrated that an asymptotic solution may be constructed within the domain of algebraic functions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528168
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