Summary: In earlier work on the one-dimensional sech\(^2\) potential energy [I. A. Howard and N. H. March, Int. J. Quantum Chem. 91, 119 (2003)] it has been shown that both electron density \(\rho(x)\) and kinetic energy \(t(x)\) are low-order polynomials in the potential \(V(x)\), for a small number of bound states. Here all attention is focused on the continuum states for the sech\(^2\) potential with a single bound state. The tool employed is the Slater sum, which satisfies a partial differential equation. This is first solved explicitly for the bound state, and then the solution is generalized to apply to the continuum. Again, considerable simplification is exhibited for this specific choice of potential. A brief discussion is included of a central sech\(^2(r)\) potential.