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Schroedinger Theory of Electrons: Complementary Perspectives (Hardcover, 1st ed. 2022)
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Schroedinger Theory of Electrons: Complementary Perspectives (Hardcover, 1st ed. 2022)
Series: Springer Tracts in Modern Physics, 285
Expected to ship within 12 - 19 working days
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This book presents a complementary perspective to Schroedinger
theory of electrons in an electromagnetic field, one that does not
appear in any text on quantum mechanics. The perspective, derived
from Schroedinger 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 Schroedinger theory emerge which
show the equation to be intrinsically self-consistent. Another
complimentary perspective to Schroedinger 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 Schroedinger 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.
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