Engineering topics
Publications and source records attributed to Epstein, S. T..
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.
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 well-known relationship between gauge invariance and current conservation is exhibited within the usual quantum mechanical formalism. It is then shown that the use of Gauge Invariant Atomic Orbitals does not necessarily lead to the expected current conservation. The reason is found to lie in the constrained nature of the gauge invariance which is provided by the use of GIAO's. It is concluded that this invariance is, of itself, no argument in favor of their use.
The well known relationship between gauge invariance and current conservation is exhibited within the usual quantum mechanical formalism. It is then shown that the use of gauge-invariant atomic orbitals (GIAO) does not necessarily lead to the expected current conservation. The reason is found to lie in the constrained nature of the gauge invariance which is provided by the use of GIAO's. It is concluded that this invariance is, of itself, no argument in favor of their use.
Various theorems in the theory of spinless particle scattering by a real central potential are derived directly from the Kohn variational principle.
Variation method, and binding energy and structure of atoms and molecules
Method of moments for determining wave functions used in calculating molecular properties
Atomic system ground state energy upper bound, considering internuclear distances and removal of restriction for negative definite potential energy operator
Exchange perturbation theories applied to delta function model of molecular hydrogen ion, discussing EL-HAV second order energy at large internuclear separations
Dipole shielding tensor of atom in arbitrary time dependent field, giving conditions for general variational calculations yielding results
Sum rule properties of finite set of wave functions obtained from application of variational principles to basis functions linear combinations
Steady state time dependent perturbation theory and variational principles
Variational method to approximate solutions of perturbation equations, perturbation analyses, and use of perturbation theory to infer variational principle
Variational method and principle
Variational method and lower bound calculations
First order wave function in 1/Z expansion
Mathematical proof of spherical symmetry of exchange potential produced by closed shell
Jacobi identity in classical mechanics