Abstract:Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann Schwinger (LS) equation is considered as a means of avoiding the shortcomings of partial-wave expansion at high energies and in the context of few-body problems. Upon the regularization of the singular kernel of the three-dimensional LS equation by a subtraction technique, a three-variate quadrature rule is used to solve the resulting nonsingular integral equation. To avoid the computational burden of discr… Show more
We present exact solutions for the Lippmann–Schwinger equation in two dimensions for circular boundary walls in three cases: (i) a finite number N of concentric barriers; (ii) a single barrier with Dirac delta derivatives, in the sense of distribution theory, namely, angular, normal, and along the curve; and (iii) a single barrier with an arbitrary distribution. As an application of this last result, we obtain conditions that must be fulfilled in order for the barrier to become invisible.
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