SOLUTION OF THE HELMHOLTZ EQUATION ON A SQUARE FOR A REACTIVE SCATTERING MODEL.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Solutions of the Helmholtz equation the second partial derivative with respect to x the second partial derivative with respect to y k squared 1psi 0 describing a simple scattering process in an L-shaped region are studied. To obtain the correct expansion for psix,y on the square corner of the L-shape when k 1, it is found necessary to replace terms sin kx sin y and sin x sin ky by sin x sin y and x cos x sin y - y cos y sin x. Terms similar to the latter have been neglected by previous authors and spurious resonances found in consequence. Author
- Numerical Mathematics
- Quantum Theory and Relativity