MARC Record from harvard_bibliographic_metadata

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008 061031s2005 enka b 000 0 eng d
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040 $aUKM$cUKM$dBAKER$dDLC
042 $aukblsr$alccopycat
050 00 $aQC174.12$b.R395 2005
082 04 $a530.12$222
100 1 $aRazavy, Mohsen.
245 10 $aClassical and dissipative quantum systems /$cMohsen Razavy.
260 $aLondon :$bImperial College Press,$cc2005.
300 $axv, 334 p. :$bill. ;$c26 cm.
504 $aIncludes bibliographical references and index.
505 0 $a1. Introduction -- 2. Phenomenological equations of motion for dissipative systems. 2.1. Frictional forces linear velocity. 2.2. Raleigh's oscillator. 2.3. One-dimensional motion and bopp transformation. 2.4. The classical theory of line width. 2.5. Frictional forces quadratic in velocity. 2.6. Non-Newtonian and nonlocal dissipative forces -- 3. Lagragian formulations. 3.1. Rayleigh and Lur'e dissipative functions. 3.2. Inverse problem of analytical dynamics. 3.3. Some examples of the Lagrangians for dissipative systems. 3.4. Non-uniqueness of the Lagrangian. 3.5. Acceptable Lagrangians for dissipative systems --
505 0 $a4. Hamiltonian formulation. 4.1. Inverse problem for the Hamiltonian. 4.2. Hamiltonians for simple dissipative systems. 4.3. Ostrogradsky's method. 4.4. Complex or leaky spring constant. 4.5. Dekker's complex coordinate formulation. 4.6. Hamiltonian formulation of the motion of a particle with variable mass. 4.7. Variable mass oscillator. 4.8. Bateman's damped-amplified harmonic oscillators. 4.9. Dissipative forces quadratic in velocity. 4.10. Resistive forces proportional to arbitrary powers of velocity. 4.11. Universal Lagrangian and Hamiltonian. 4.12. Hamiltonian formulation in phase space of N-dimensions. 4.13. Symmetric phase space formulation of the damped harmonic oscillator. 4.14. Dynamical systems expressible as linear difference equations -- 5. Hamilton-Jacobi formulation. 5.1. The Hamilton-Jacobi equation for linear damping. 5.2. Classical action for an oscillator with leaky spring constant. 5.3. More about the Hamilton-Jacobi equation for the damped motion --
505 0 $a6. Motion of a charged particle in an external electromagnetic field in the presence of damping -- 7. Noether and non-Noether symmetries and conservation laws. 7.1. Non-Noether symmetries and conserved quantities. 7.2. Noether's theorem for a scalar field -- 8. Dissipative forces derived from many-body problems. 8.1. The Schrodinger chain. 8.2. A particle coupled to a chain. 8.3. Dynamics of a non-uniform chain. 8.4. Mechanical system coupled to a heat bath. 8.5. Euclidean Lagrangian -- 9. A particle coupled to a field. 9.1. Harmonically bound radiating electron. 9.2. An oscillator coupled to a string of finite length. 9.3. An oscillator coupled to an infinite string -- 10. Damped motion of the central particle. 10.1. Diagonalization of the Hamiltonian -- 11. Classical microscopic models of dissipation and minimal coupling rule --
505 0 $a12. Quantization of the dissipative systems. 12.1. Early attempts to quantize the damped oscillator. 12.2. Yang-Feldman method of quantization. 12.3. Heisenberg's equations of motion for Dekker's formulation. 12.4. Quantization of the Bateman Hamiltonian. 12.5. Fermi's nonlinear equation for quantized radiation reaction. 12.6. Attempts to quantize systems with a dissipative force quadratic in velocity. 12.7. Solution of the wave equation for linear and Newtonian damping forces. 12.8. The classical limit of the Schrodinger equation with velocity-dependent forces. 12.9. Quadratic damping as an externally applied force. 12.10. Motion in a viscous field of force proportional to an arbitrary power of velocity. 12.11. The classical limit and the Van Vleck determinant --
505 0 $a13. Quantization of explicitly time-dependent Hamiltonian. 13.1. Wave equation for the Kanai-Caldirola Hamiltonian. 13.2. Coherent states of a damped oscillator. 13.3. Squeezed state of a damped harmonic oscillator. 13.4. Quantization of a system with variable mass. 13.5. The Schrodinger-Langevin equation for linear damping. 13.6. An extension of the Madelung formulation. 13.7. Quantization of a modified Hamilton-Jacobi equation for damped systems. 13.8. Exactly solvable cases of the Schrodinger-Langevin equation. 13.9. Harmonically bound radiating electron and the Schrodinger-Langevin equation. 13.10. Other phenomenological nonlinear potentials for dissipative systems. 13.11. Scattering in the presence of frictional forces. 13.12. Application of the Noether theorem: linear and nonlinear wave equations for dissipative systems. 13.3. Wave equation for impulsive forces acting at certain intervals. 13.14. Classical limit for the time-dependent problems --
505 0 $a14. Density matrix and the Wigner distribution function. 14.1. Classical distribution function for nonconservative motions. 14.2. The density matrix. 14.3. Phase space quantization of Dekker's Hamiltonian. 14.4. Density operator and the Fokker-Planck equation. 14.5. The density matrix formulation of a solvable model. 14.6. Wigner distribution function for the damped oscillator. 14.7. Density operator for a particle coupled to a heat bath -- 15. Path integral formulation of a damped harmonic oscillator. 15.1. Propagator for the damped harmonic oscillator. 15.2. Path integral quantization of a harmonic oscillator with complex string constant. 15.3. Modified classical action and the propagator for the damped harmonic oscillator. 15.4. Path integral formulation of a system coupled to a heat bath --
505 0 $a16. Quantization of the motion of an infinite chain. 16.1. Quantum mechanics of a uniform chain. 16.2. Ground state of the central particle. 16.3. Wave equation for a non-uniform chain. 16.4. Connection with other phenomenological frictional forces. 16.5. Fokker-Planck equation for the probability density -- 17. The Heisenberg equations of motion for a particle coupled to a heat bath. 17.1. Heisenberg equations for a damped harmonic oscillator. 17.2. Density matrix for the motion of a particle coupled to a field. 17.3. Equations of motion for the central particle. 17.4. Wave equation for the motion of the central particle. 17.5. Motion of the center-of-mass in viscous medium. 17.6. Invariance under Galilean transformation. 17.7. Velocity coupling and coordinate coupling. 17.8. Equation of motion for a harmonically bound radiating electron --
505 0 $a18. Quantum mechanical models of dissipative systems. 18.1. Forced vibration with damping. 18.2. The Wigner-Weisskopf model. 18.3. Quantum theory of line width. 18.4. The optical potential. 18.5. Gisin's nonlinear wave equation. 18.6. Nonlinear generalization of the wave equation. 18.7. Dissipation arising from the motion of the boundaries. 18.8. Decaying states in a many-Boson system -- 19. More on the concept of optical potential. 19.1. The classical analogue of the nonlocal interaction. 19.2. Minimal and/or maximal coupling. 19.3. Damped harmonic oscillator and optical potential. 19.4. Quantum mechanical analogue of the Raleigh oscillator.
650 0 $aEnergy dissipation.
650 0 $aQuantum theory.
650 0 $aMathematical physics.
650 0 $aHamiltonian systems.
650 0 $aDifferential equations, Partial.
988 $a20070802
906 $0OCLC