Upon introducing the outgoing spherical (or circular cylinder) partial waves {ψn} as a basis, the equationQT= − Re (Q) is obtained for the transition matrixTdescribing scattering for general incidence on a smooth object of arbitrary shape. Elements ofQinvolve integrals over the object surface, e.g.Qmn = ±(i2)δmn+(k8π)∫dσ⋅∇[Re(ψm)ψn]. where the −, + apply for Dirichlet and Neumann conditions, respectively. For quadric (separable) surfaces,Qis symmetric. Symmetry and unitarity lead to a secular equation defining eigenfunctions for general bodies. Some apparently new closed‐form results are obtained in the low frequency limit, and the transition matrix is computed numerically for the infinite strip.