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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Quantum Theory from a Nonlinear Perspective - Riccati Equations in Fundamental Physics (Hardcover, 1st ed. 2018)
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Quantum Theory from a Nonlinear Perspective - Riccati Equations in Fundamental Physics (Hardcover, 1st ed. 2018)
Series: Fundamental Theories of Physics, 191
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This book provides a unique survey displaying the power of Riccati
equations to describe reversible and irreversible processes in
physics and, in particular, quantum physics. Quantum mechanics is
supposedly linear, invariant under time-reversal, conserving energy
and, in contrast to classical theories, essentially based on the
use of complex quantities. However, on a macroscopic level,
processes apparently obey nonlinear irreversible evolution
equations and dissipate energy. The Riccati equation, a nonlinear
equation that can be linearized, has the potential to link these
two worlds when applied to complex quantities. The nonlinearity can
provide information about the phase-amplitude correlations of the
complex quantities that cannot be obtained from the linearized
form. As revealed in this wide ranging treatment, Riccati equations
can also be found in many diverse fields of physics from
Bose-Einstein-condensates to cosmology. The book will appeal to
graduate students and theoretical physicists interested in a
consistent mathematical description of physical laws.
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