Interdeterminancy of basin and surface properties of an open system

Abstract

This paper delineates and illustrates an important physical consequence of the Heisenberg equation of motion governing the expectation value of an observable for a proper open system, one whose basin is bounded by a surface of zero flux in the gradient vector field of the electron density. For a system in a stationary state, this theorem derives from the variation of Schrödinger's energy functional over an open system. The variation demonstrates that the surface of the open system, as well as the wave function and energy of the total system, are simultaneously stationary with respect to any and all variations δ ψ , corresponding to a stationarity with respect to any and all physical perturbations -(i ε/ Planck's constant) G caret ψ caused by a generator G caret. Thus the properties of a proper open system are dependent upon its surface and vice versa, the theorem equating the expectation value of the commutator of the Hamiltonian and a generator G caret for the open system to the flux in the current density for G caret through its surface. The criticisms of the interdependence of the basin and surface properties of a proper open system that appeared recently in this journal are refuted, including the argument that mutiplication of an electron density by a constant factor yields a density for a different system. The consequences of this interdependence in the construction of a polypeptide through the use of amino acid residues defined as proper open systems is discussed and illustrated through the explicit calculation of the properties of the C|N interatomic surfaces of the amidic bonds. It is demonstrated that the the degree of transferability of a residue is determined by the degree of similarity in the properties of its two bounding amidic surfaces.Key words: electron density, ransferability of density, atoms in molecules, zero flux surface.