Hyperspherical 10 Hyperspherical coordinates 10 Wave functions 10 Sturmian 8 Transition amplitudes 8 Dinger equation 6 Calculations 4 Double ionization 4 High-energy electron 4 Impact ionization 4 Non-homogeneous 4 Scattering problems 4 Scattering process 4 Spherical coordinates 4 Three body 4 Three-body wave functions 4 Analytic expressions 2 Analytical expressions 2 Analytical results 2 Asymptotic analysis 2 Asymptotic behaviour 2 Asymptotic limits 2 Atoms 2 Basis functions 2 Basis sets 2 Bound state 2 Closed form solutions 2 Collision problem 2 Collision process 2 Computational requirements 2