Engineering topics
Publications and source records attributed to Eaves, J. O..
An objection to the effect that the first-order orbitals describing the perturbation of Hartree-Fock or X-alpha closed shell atoms by a multipole electric field may not have the required symmetry properties is acknowledged and answered. It is shown that the assumption of the expected symmetry is a self-consistent one.
Calculations for the ground states of H, He, and Be, conducted by Steiner and Sykes (1972), show that the inclusion of a very small number of cusp functions can lead to a substantial enhancement of the quality of the Gaussian basis used in molecular wavefunction computations. The properties of the cusped-Gaussian basis are investigated by a calculation of lower bounds concerning the ground state energy of the hydrogen atom.
It is shown that the first order orbitals for X-alpha or Hartree-Fock atoms perturbed by multipole electric fields have the expected symmetry properties.
The solution of the one dimensional, time independent, Schroedinger equation in which the energy minus the potential varies as the nth power of the distance is obtained from proper linear combinations of Bessel functions. The linear combinations called generalized Airy functions, reduce to the usual Airy functions Ai(x) and Bi(x) when n equals 1 and have the same type of simple asymptotic behavior. Expressions for the generalized Airy functions which can be evaluated by the method of generalized Gaussian quadrature are obtained.