Schroedinger Theory of Electrons: Complementary Perspectives

This book presents a new perspective on Schrödinger theory of electrons in an electromagnetic field, derived from the individual electron's temporal and stationary-state equations of motion. It reveals physical insights and new properties of the electronic system, and provides a rigorous physical explanation of the mapping from the interacting system to the local potential theory equivalent. The new perspectives are elucidated by application to analytically solvable interacting systems, and solutions and other relevant wave function properties are derived.

Format: Hardback
Length: 407 pages
Publication date: 08 July 2022
Publisher: Springer Nature Switzerland AG

This book presents a comprehensive and insightful perspective on Schrödinger theory of electrons in an electromagnetic field, offering a viewpoint that is not readily found in any text on quantum mechanics. The perspective, derived from Schrödinger's theory, revolves around the individual electron's journey within the sea of electrons, utilizing its temporal and stationary-state equations of motion. These equations constitute the 'Quantal Newtonian Second and First Laws.' The Laws are expressed in terms of 'classical fields' experienced by each electron, with the sources of these fields being quantum-mechanical expectation values of Hermitian operators calculated with respect to the electron's wave function. Each electron encounters not only the external field but also internal fields that represent the system's properties, as well as a field that captures its response. The energies of the electronic system are derived from these fields.

The 'Quantal Newtonian Laws' yield profound physical insights, unveiling new properties of the electronic system. Furthermore, they lead to the development of new mathematical understandings of Schrödinger theory, demonstrating that the equation is inherently self-consistent.

Another complementary perspective to Schrödinger theory is its manifestation as a local effective potential theory, described through Quantal Density Functional theory. This description, too, revolves around 'classical fields' and 'quantal sources.' The theory provides a rigorous physical explanation for the mapping from an interacting system to its local potential theory equivalent.

The complementary perspective to stationary ground state Schrödinger 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 through the application of these theories to analytically solvable interacting systems. These solutions, along with other insightful examples, serve to deepen our understanding of the subject matter and broaden our horizons in the realm of quantum mechanics.

Weight: 778g
Dimension: 162 x 242 x 30 (mm)
ISBN-13: 9783030974084
Edition number: 1st ed. 2022