Classical and Quantum Euler Equation

The book is devoted to mathematical description of
damped oscillations and their relation with the
Euler equation. This equation has been studied by
Leonard Euler starting from 1740 and also is known
as the Cauchy-Euler equidimensional equation.
To develop the Lagrangian and the Hamiltonian
formalism extension of analytical
mechanics to pseudo-Riemannian metrics is
introduced. Depending on
self-adjoint properties of variational functional,
two different descriptions are presented. One of
them, called the dual Bateman system, supply a
damped system with its time reversal image. The
second one imitates damping by the time dependent
mass of the system. Quantization of damped
oscillator and wide class of exactly solvable
nonlinear quantum Euler problems are treated in
details. Intriguing relations with Chern-Simons
topological quantum mechanics and soliton theory are
indicated.
The book is self contained and
pedagogically written as an introduction to the
subject for students at advanced undergraduate and
graduate level from science and engineering
specialties. Also it could be a valuable source for
researchers in the field.

Autorentext

Neslihan Eti, MSc in Mathematics and Research assistant at Izmir
Institute of Technology. Field of study: photonic crystals.
Oktay K. Pashaev, Diploma in Physics - Moscow State University,
PhD - JINR, Dubna: Professor of Mathematics at Izmir Institute of
Technology, Turkey. Fields of study: integrable systems, solitons
and quantum physics.

Klappentext

The book is devoted to mathematical description of
damped oscillations and their relation with the
Euler equation. This equation has been studied by
Leonard Euler starting from 1740 and also is known
as the Cauchy-Euler equidimensional equation.
To develop the Lagrangian and the Hamiltonian
formalism extension of analytical
mechanics to pseudo-Riemannian metrics is
introduced. Depending on
self-adjoint properties of variational functional,
two different descriptions are presented. One of
them, called the dual Bateman system, supply a
damped system with its time reversal image. The
second one imitates damping by the time dependent
mass of the system. Quantization of damped
oscillator and wide class of exactly solvable
nonlinear quantum Euler problems are treated in
details. Intriguing relations with Chern-Simons
topological quantum mechanics and soliton theory are
indicated.
The book is self contained and
pedagogically written as an introduction to the
subject for students at advanced undergraduate and
graduate level from science and engineering
specialties. Also it could be a valuable source for
researchers in the field.