Truncated Invariance Groups for Stable Molecules

Abstract

The concept of a concentrated wavefunction originally proposed by Watson has been elaborated into a theory of a Hilbert space of concentrated wavefunctions called the function space of square‐integrable functions on a truncated support. When the operators of the full invariance group of the Hamiltonian are restricted to this function space a partial collapse of the group takes place leading in a natural way to a truncated group which is identical to the Longuet‐Higgins group for the system. Hence a more precise meaning is attached to the concept of feasibility proposed by Longuet‐Higgins. Another property of the Hilbert space mentioned is that it gives mathematical significance to the concept of a model so extensively used in molecular quantum mechanics.