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5-states adm+ analytic approximations Bartlett boundary conditions choice coefficients will vanish consecutive coefficients constant contains only positive contravariant derivatives dimension length discussion DISSERTATION IN PHYSICS DOCTOR OF PHILOSOPHY E. A. HYLLERAAS E. E. Witmer eigenvalue electrons equation is regular Equations 21 Euler equation exist F and G F or G fm and gm FRED GEORGE ground state eigenfunction homogeneous with exponent independent variables infinite number infinite realm inseparability kinetic energy letter will represent lowest power mathematical nucleus numerical value obtained ordinary differential equation origin partial differential equation PHILADELPHIA 1936 Phys pole positive integral powers possible potential energy problem properties pure ratios quadratic form radius of convergence relation between F Schroedinger equation separable variable set of variables Set up solutions solutions convergent symmetry tensor third quantum number transformation TWO-ELECTRON ATOM V)gm vanish identically variable of dimension variable of physical wave function Zeits zeroth power