Quantum Mechanical Model of Three-Body Rearrangement Scattering. I. Formal Solution of the Helmholtz Equation on a Square

Solutions of the Helmholtz equation (∂2 / ∂x2 + ∂2 / ∂y2 + k2 + 1)Ψ = 0 describing a simple scattering process in an L-shaped region are studied. To obtain the correct expansion for ψ(x, y) on the square corner of the L shape when k = 1, it is found necessary to replace terms sinkx siny and sinx sinky by sinx siny and (x cosx siny–y cosy sinx). Terms similar to the latter have been neglected by previous authors and spurious resonances found in consequence.