Abstract
Generalized variational equations are derived for calculating the elastic and inelastic scattering amplitudes associated with the scattering of electrons by hydrogen atoms. The derivation of these equations is such that no unnecessary restrictions are imposed on possible trial wave functions. Two equivalent formulations are given: one involving the use of symmetrized wave functions; the other involving wave functions of the conventional (Mott and Massey) type. For trial wave functions consisting of only the incident wave (multiplied by a hydrogen eigenfunction), these variational equations yield the same results as are obtained by the approximations of Born and Oppenheimer. Various calculation procedures are discussed.In an appendix, it is shown that the Hulth\`en variational equation for the scattering phases is a special case of the Kohn variational equation for the scattering amplitude.
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