On the global nature of the semiclassical wavefunction describing elastic scattering in several coordinate dimensions

The short-wavelength (semiclassical) limit of the quantal wavefunction in a multidimensional euclidean configuration space is discussed. Attention is drawn to the shortcomings of some previous approaches with regard to the treatment of multivaluedness and caustics. A global representation of the wavefunctions based on generalised Kirchoff diffraction integrals is proposed. Application of the saddle-point approximation leads to a local semiclassical representation of the wavefunction as a series of JWKB approximations. (Auth.)