Schrdinger Theory of Electrons: Complementary Perspectives

This book presents a complementary perspective to Schrdinger theory of electrons in an electromagnetic field, one that does not appear in any text on quantum mechanics. The perspective, derived from Schrdinger theory, is that of the individual electron in the sea of electrons via its temporal and stationary-state equations of motion the Quantal Newtonian Second and First Laws. The Laws are in terms of classical fields experienced by each electron, the sources of the fields being quantum-mechanical expectation values of Hermitian operators taken with respect to the wave function. Each electron experiences the external field, and internal fields representative of properties of the system, and a field descriptive of its response. The energies are obtained in terms of the fields. The Quantal Newtonian Laws lead to physical insights, and new properties of the electronic system are revealed. New mathematical understandings of Schrdinger theory emerge which show the equation to be intrinsically self-consistent. Another complimentary perspective to Schrdinger theory is its manifestation as a local effective potential theory described via Quantal Density Functional theory. This description too is in terms of classical fields and quantal sources. The theory provides a rigorous physical explanation of the mapping from the interacting system to the local potential theory equivalent. The complementary perspective to stationary ground state Schrdinger theory founded in the theorems of Hohenberg and Kohn, their extension to the presence of a magnetic field and to the temporal domain Modern Density Functional Theory -- is also described. The new perspectives are elucidated by application to analytically solvable interacting systems. These solutions and other relevant wave function properties are derived.