Quantum theory from a nonlinear perspective : Riccati equations in fundamental physics /: Riccati equations in fundamental physics. (2018)

• Record Type: Book
• Further Information: Note: Dieter Schuch.
• Authors: Schuch, Dieter
• Contents: Intro; Preface; Contents; 1 Introduction; References; 2 Time-Dependent SchrÃœdinger Equation and Gaussian Wave Packets; 2.1 Dynamics of Mean Values and Uncertainties; 2.2 Direct Solution of the Riccati Equation; 2.3 Alternative Treatment via the Ermakov Equation Â#x83;; 2.3.1 Position and Momentum Uncertainties in Terms of Ermakov and Riccati Variables; 2.3.2 Consequences of the Wave Packet Spreading for the Probability Current; 2.4 Linearization of the Complex Riccati Equation; 2.5 Time-Dependent Green Function or Feynman Kernel. 2.5.1 Riccati Equations from the Green Function and Trigonometric Considerations2.6 Lagrange -- Hamilton Formalism for Quantum Uncertainties; 2.7 Momentum Space Representation; 2.8 Wigner Function and Ermakov Invariant; 2.9 Representation of Canonical Transformations in Quantum Mechanics; 2.10 Algebraic Derivation of the Ermakov Invariant; 2.11 Generalized Creation and Annihilation Operators and Coherent States; 2.12 Application of the Ermakov Invariant to Transform Â#x83;; 2.13 Interrelations Between the Different Treatments Â#x83;; References; 3 Time-Independent SchrÃœdinger and Riccati Equations. 3.1 On Supersymmetry and Riccati Equations3.2 Nonlinear Version of Time-Independent Quantum Mechanics; 3.3 Complex Hamiltonians with Real Spectra; 3.4 Comparison of Time-Dependent and Time-Independent Systems; References; 4 Dissipative Systems with Irreversible Dynamics; 4.1 Different Approaches for Treating Open Dissipative Systems; 4.2 System-Plus-Reservoir Approaches; 4.2.1 Caldeira -- Leggett Model and Kossakowski -- Lindblad Generators; 4.2.2 Bateman Hamiltonian; 4.3 Effective Models Within the Canonical Formalism; 4.3.1 Caldirola -- Kanai Hamiltonian; 4.3.2 Expanding Coordinate System. 4.4 Effective Models Using Nonlinear Modifications of the SchrÃœdinger Equation4.4.1 Models Based on Ehrenfest's Theorem and the Langevin Equation; 4.4.2 Models Based on Non-unitary Time-Evolution; 4.4.3 Models Based on a Smoluchowski Equation for the Probability Density; 4.5 Non-unitary Connections Between the Canonical and Nonlinear Approaches; References; 5 Irreversible Dynamics and Dissipative Energetics of Gaussian Wave Packet Solutions; 5.1 Direct Solution of the Riccati Equation, Ermakov Equation and Corresponding Invariant. 5.2 Position and Momentum Uncertainties in Terms of Ermakov Â#x83;5.3 Linearization of the Riccati Equation and Dissipative Lagrange -- Hamilton Â#x83;; 5.4 New Qualitative Quantum Effects Induced by a Dissipative Environment; 5.4.1 Increase of Ground State Energy Due to Interaction with an Environment; 5.4.2 Bifurcation and Non-diverging Uncertainty Product; 5.4.3 Modified Plane Waves and Nonlinear Superposition; 5.4.4 Environmentally-Induced Tunnelling Currents and Resonant Energy Back-Transfer; 5.5 Time-Dependent Green Function for the Dissipative Case.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 515/.35; Physics; Riccati equation; Quantum theory -- Mathematics; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Quantum theory -- Mathematics; Riccati equation; Physics; Quantum Physics; Applications of Nonlinear Dynamics and Chaos Theory; Ordinary Differential Equations; History and Philosophical Foundations of Physics; Science -- Chaotic Behavior in Systems; Mathematics -- Differential Equations; Science -- Physics; Nonlinear science; Differential calculus & equations; History of science; Quantum theory; Differential Equations; Science -- Quantum Theory; Quantum physics (quantum mechanics & quantum field theory); Electronic books; Electronic book
• Languages: English
• ISBNs: 9783319655949; 3319655949
• Related ISBNs: 9783319655925; 3319655922
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed January 25, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.