Permutation Of Coordinates Research Articles

A note on my paper: “On symmetric matrices whose eigenvalues satisfy linear inequalities”

The first part of the theorem of the above paper states that if ois a closed convex set in real X1 ... Xn-space which is invariant under permutations of coordinates, and if C(o-) denotes the set of real symmetric nXn matrices whose eigenvalues X1, X. form the coordinates of points in a, then C(o) is convex. I am obliged to Professor R. T. Rockafellar for pointing out that this statement is essentially contained in a theorem of Chandler Davis.2 The statement also follows from an earlier result of V. B. Lidskii,3 which was not known to me at the time of publication.

Perturbation Theory for Intermolecular Interactions in the Wave-Operator Formalism

A Schrödinger-type perturbation theory for intermolecular or interatomic interactions is developed in the wave-operator formalism. To include all exchange effects, wavefunctions are used whose symmetry with respect to permutations of both electronic and nuclear coordinates can be prescribed arbitrarily. This necessitates a modification of the usual perturbation theory. The interaction energy is obtained as a series in ascending powers of the interaction operator. It is proved that every term in this series is real and that the terms of even order are negative definite for perturbation of the ground state. It is verified that up to and including third order the results of this theory, if they are restricted to electron exchange only, agree exactly with those of the Eisenschitz—London theory.

Classification of triton wave functions

A classification of all angular momentum-isobaric spin functions which can be present in the ground state wave function of H3 is carried out by methods of group theory. This classification, based on the behaviour of the functions under rotations of the co-ordinate axes and permutations of the three nucleons, yields three S-state functions, four P-state functions and three D-state functions. All ten states are present in H3 if non-central forces exist between nucleons.