INTERDETERMINANCY OF BASIN AND SURFACE-PROPERTIES OF AN OPEN SYSTEM

This paper delineates and illustrates an important physical consequenc e 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 electro n density. For a system in a stationary state, this theorem derives fr om the variation of Schrodinger's energy functional over an open syste m. The variation demonstrates that the surface of the open system, as well as the wave function and energy of the total system, are simultan eously stationary with respect to any and all variations delta psi, co rresponding to a stationarity with respect to any and all physical per turbations -(i epsilon/h)(G) over cap psi caused by a generator (G) ov er cap. Thus the properties of a proper open system are dependent upon its surface and vice versa, the theorem equating the expectation valu e of the commutator of the Hamiltonian and a generator (G) over cap fo r the open system to the flux in the current density for (G) over cap through its surface. The criticisms of the interdependence of the basi n and surface properties of a proper open system that appeared recentl y in this journal are refuted, including the argument that mutiplicati on of an electron density by a constant factor yields a density for a different system. The consequences of this interdependence in the cons truction of a polypeptide through the use of amino acid residues defin ed as proper open systems is discussed and illustrated through the exp licit calculation of the properties of the CIN interatomic surfaces of the amidic bonds. It is demonstrated that the the degree of transfera bility of a residue is determined by the degree of similarity in the p roperties of its two bounding amidic surfaces.