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Quantum Theory from a Nonlinear Perspective

Part of the Fundamental Theories of Physics Book Series (volume 191)

DOI: 10.1007/978-3-319-65594-9

ISBN: 978-3-319-65592-5

Publisher: Springer International Publishing - Springer Journals

Jan 21, 2018

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Introduction

Schuch, Dieter

Pages: 1 –8

[An attempt to look at quantum theory from a different perspective also leads to the question of where the idea of “quantization”, i.e., dividing our material world into “smallest building blocks”, actually originates.]
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Time-Dependent Schrödinger Equation and Gaussian Wave Packets

Schuch, Dieter

Pages: 9 –67

[In the following, the one-dimensional time-dependentFrequencytime-dependentSchrödinger equationSchrödinger equation (TDSE) EquationSchrödinger for problems with analytic solutions in the form of GaussianGaussian wave packetsGaussianwave packet (WPs) is considered.]
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Time-Independent Schrödinger and Riccati Equations

Schuch, Dieter

Pages: 69 –83

[In Sect. 2.11itEquationSchrödinger has been shown how a generalization of the creation and annihilation operators, known from the algebraic treatment of the harmonicOscillatorharmonic oscillator (HO) Harmonic oscillator (HO) problem.]
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Dissipative Systems with Irreversible Dynamics

Schuch, Dieter

Pages: 85 –131

[Classical Hamiltonian mechanicsClassicalmechanicsandMechanics quantum mechanics describe isolated systemsIsolated system with reversible dynamics and (for not explicitly time-dependent (TD) potentials) conservation of energy.]
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Irreversible Dynamics and Dissipative Energetics of Gaussian Wave Packet Solutions

Schuch, Dieter

Pages: 133 –177

[InDissipativeenergeticsthisEquationRiccatisectionIrreversible the same one-dimensional problems as in Sect. 5.2 will be considered, particularly theHarmonic oscillator (HO) harmonic oscillator (HO) withFrequencyconstant constant frequency \documentclass[12pt]{minimal} \usepackage{amsmath}...
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Dissipative Version of Time-Independent Nonlinear Quantum Mechanics

Schuch, Dieter

Pages: 179 –185

[In the time-dependent (TD) non-dissipative caseNon-dissipative, the information on the time-evolution of the wave.]
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Nonlinear Riccati Equations in Other Fields of Physics

Schuch, Dieter

Pages: 187 –209

[In Chap. 2 it has been shown that, for systems where the time-dependent Schrödinger equation (TDSE) possesses analytic solutions (i.e., at most quadratic Hamiltonians), the information about the dynamics of the classical as well as quantum mechanical aspects of the system can equally well be...
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Summary, Conclusions and Perspectives

Schuch, Dieter

Pages: 211 –228

[The opening Chaps. (1–3) embark upon a nonlinear (NL) reformulation ofDifferential equationnonlinear (NL) quantum mechanicsEquationnonlinear in terms of complex Riccati orSupersymmetricquantum mechanics the equivalent realRiccati equationreal Ermakov equations. EquationErmakovToErmakovequation...

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