An important model in the study of electron-atom collisions was development by Temkin and Poet. Although the model has been used to test many theories and approximation methods, the novel method of solution used by Poet has not been developed further to any great extent. The Temkin-Poet model of electron scattering simplifies the three-body scattering problem by suppressing all angular dependence of the wavefunction. In this thesis we return to Poet's method and apply it to a range of calculations for the hydrogen-isoelectronic series. Firstly it is demonstrated that the method provides high-precision solutions for elastic and inelastic scattering. these solutions will then be used to investigate various aspects of electron scattering including the ionisation of hydrogen in the near-threshold region, resonant states in helium, and the scaling of elastic cross sections for a number of hydrogen-like ions.