| Preface | p. v |
| Linear Quantum Mechanics: Its Successes and Problems | p. 1 |
| The Fundamental Hypotheses of the Linear Quantum Mechanics | p. 1 |
| Successes and Problems of the Linear Quantum Mechanics | p. 5 |
| Dispute between Bohr and Einstein | p. 10 |
| Analysis on the Roots of Problems of Linear Quantum Mechanics and Review on Recent Developments | p. 15 |
| Bibliography | p. 21 |
| Macroscopic Quantum Effects and Motions of Quasi-Particles | p. 23 |
| Macroscopic Quantum Effects | p. 23 |
| Macroscopic quantum effect in superconductors | p. 23 |
| Quantization of magnetic flux | p. 24 |
| Structure of vortex lines in type-II superconductors | p. 25 |
| Josephson effect | p. 26 |
| Macroscopic quantum effect in liquid helium | p. 28 |
| Other macroscopic quantum effects | p. 31 |
| Quantum Hall effect | p. 31 |
| Spin polarized atomic hydrogen system | p. 33 |
| Bose-Einstein condensation of excitons | p. 33 |
| Analysis on the Nature of Macroscopic Quantum Effect | p. 34 |
| Motion of Superconducting Electrons | p. 47 |
| Motion of electrons in the absence of external fields | p. 49 |
| Motion of electrons in the presence of an electromagnetic field | p. 50 |
| Analysis of Macroscopic Quantum Effects in Inhomogeneous Superconductive Systems | p. 54 |
| Proximity effect | p. 54 |
| Josephson current in S-I-S and S-N-S junctions | p. 56 |
| Josephson effect in SNIS junction | p. 59 |
| Josephson Effect and Transmission of Vortex Lines Along the Superconductive Junctions | p. 60 |
| Motion of Electrons in Non-Equilibrium Superconductive Systems | p. 66 |
| Motion of Helium Atoms in Quantum Superfluid | p. 72 |
| Bibliography | p. 77 |
| The Fundamental Principles and Theories of Nonlinear Quantum Mechanics | p. 81 |
| Lessons Learnt from the Macroscopic Quantum Effects | p. 81 |
| Fundamental Principles of Nonlinear Quantum Mechanics | p. 84 |
| The Fundamental Theory of Nonlinear Quantum Mechanics | p. 89 |
| Principle of nonlinear superposition and Backlund transformation | p. 89 |
| Nonlinear Fourier transformation | p. 94 |
| Method of quantization | p. 95 |
| Nonlinear perturbation theory | p. 100 |
| Properties of Nonlinear Quantum-Mechanical Systems | p. 101 |
| Bibliography | p. 106 |
| Wave-Corpuscle Duality of Microscopic Particles in Nonlinear Quantum Mechanics | p. 109 |
| Invariance and Conservation Laws, Mass, Momentum and Energy of Microscopic Particles in the Nonlinear Quantum Mechanics | p. 110 |
| Position of Microscopic Particles and Law of Motion | p. 117 |
| Collision between Microscopic Particles | p. 126 |
| Attractive interaction (b [greater than sign] 0) | p. 126 |
| Repulsive interaction (b [less than sign] 0) | p. 136 |
| Numerical simulation | p. 139 |
| Properties of Elastic Interaction between Microscopic Particles | p. 143 |
| Mechanism and Rules of Collision between Microscopic Particles | p. 149 |
| Collisions of Quantum Microscopic Particles | p. 154 |
| Stability of Microscopic Particles in Nonlinear Quantum Mechanics | p. 161 |
| "Initial" stability | p. 162 |
| Structural stability | p. 164 |
| Demonstration on Stability of Microscopic Particles | p. 169 |
| Multi-Particle Collision and Stability in Nonlinear Quantum Mechanics | p. 173 |
| Transport Properties and Diffusion of Microscopic Particles in Viscous Environment | p. 178 |
| Microscopic Particles in Nonlinear Quantum Mechanics versus Macroscopic Point Particles | p. 188 |
| Reflection and Transmission of Microscopic Particles at Interfaces | p. 193 |
| Scattering of Microscopic Particles by Impurities | p. 200 |
| Tunneling and Fraunhofer Diffraction | p. 209 |
| Squeezing Effects of Microscopic Particles Propagating in Nonlinear Media | p. 218 |
| Wave-corpuscle Duality of Microscopic Particles in a Quasiperiodic Perturbation Potential | p. 221 |
| Bibliography | p. 228 |
| Nonlinear Interaction and Localization of Particles | p. 233 |
| Dispersion Effect and Nonlinear Interaction | p. 233 |
| Effects of Nonlinear Interactions on Behaviors of Microscopic Particles | p. 238 |
| Self-Interaction and Intrinsic Nonlinearity | p. 243 |
| Self-localization of Microscopic Particle by Inertialess Self-interaction | p. 250 |
| Nonlinear Effect of Media and Self-focusing Mechanism | p. 252 |
| Localization of Exciton and Self-trapping Mechanism | p. 258 |
| Initial Condition for Localization of Microscopic Particle | p. 263 |
| Experimental Verification of Localization of Microscopic Particle | p. 267 |
| Observation of nonpropagating surface water soliton in water troughs | p. 269 |
| Experiment on optical solitons in fibers | p. 272 |
| Bibliography | p. 274 |
| Nonlinear versus Linear Quantum Mechanics | p. 277 |
| Nonlinear Quantum Mechanics: An Inevitable Result of Development of Quantum Mechanics | p. 277 |
| Relativistic Theory and Self-consistency of Nonlinear Quantum Mechanics | p. 281 |
| Bound state and Lorentz relations | p. 283 |
| Interaction between microscopic particles in relativistic theory | p. 286 |
| Relativistic dynamic equations in the nonrelativistic limit | p. 288 |
| Nonlinear Dirac equation | p. 291 |
| The Uncertainty Relation in Linear and Nonlinear Quantum Mechanics | p. 292 |
| The uncertainty relation in linear quantum mechanics | p. 292 |
| The uncertainty relation in nonlinear quantum mechanics | p. 293 |
| Energy Spectrum of Hamiltonian and Vector Form of the Nonlinear Schrodinger Equation | p. 303 |
| General approach | p. 304 |
| System with two degrees of freedom | p. 306 |
| Perturbative method | p. 309 |
| Vector nonlinear Schrodinger equation | p. 313 |
| Eigenvalue Problem of the Nonlinear Schrodinger Equation | p. 315 |
| Microscopic Causality in Linear and Nonlinear Quantum Mechanics | p. 321 |
| Bibliography | p. 326 |
| Problem Solving in Nonlinear Quantum Mechanics | p. 329 |
| Overview of Methods for Solving Nonlinear Quantum Mechanics Problems | p. 329 |
| Inverse scattering method | p. 330 |
| Backlund transformation | p. 330 |
| Hirota method | p. 331 |
| Function and variable transformations | p. 331 |
| Function transformation | p. 331 |
| Variable transformation and characteristic line | p. 332 |
| Other variable transformations | p. 332 |
| Self-similarity transformation | p. 333 |
| Galilei transformation | p. 334 |
| Traveling-wave method | p. 335 |
| Perturbation method | p. 335 |
| Variational method | p. 335 |
| Numerical method | p. 335 |
| Experimental simulation | p. 335 |
| Traveling-Wave Methods | p. 336 |
| Nonlinear Schrodinger equation | p. 336 |
| Sine-Gordon equation | p. 337 |
| Inverse Scattering Method | p. 340 |
| Perturbation Theory Based on the Inverse Scattering Transformation for the Nonlinear Schrodinger Equation | p. 345 |
| Direct Perturbation Theory in Nonlinear Quantum Mechanics | p. 352 |
| Method of Gorshkov and Ostrovsky | p. 352 |
| Perturbation technique of Bishop | p. 356 |
| Linear Perturbation Theory in Nonlinear Quantum Mechanics | p. 358 |
| Nonlinear Schrodinger equation | p. 359 |
| Sine-Gordon equation | p. 364 |
| Nonlinearly Variational Method for the Nonlinear Schrodinger Equation | p. 366 |
| D Operator and Hirota Method | p. 375 |
| Backlund Transformation Method | p. 379 |
| Auto-Backlund transformation method | p. 379 |
| Backlund transform of Hirota | p. 382 |
| Method of Separation of Variables | p. 384 |
| Solving Higher-Dimensional Equations by Reduction | p. 387 |
| Bibliography | p. 394 |
| Microscopic Particles in Different Nonlinear Systems | p. 397 |
| Charged Microscopic Particles in an Electromagnetic Field | p. 397 |
| Microscopic Particles Interacting with the Field of an External Traveling Wave | p. 401 |
| Microscopic Particle in Time-dependent Quadratic Potential | p. 404 |
| 2D Time-dependent Parabolic Potential-field | p. 411 |
| Microscopic Particle Subject to a Monochromatic Acoustic Wave | p. 415 |
| Effect of Energy Dissipation on Microscopic Particles | p. 419 |
| Motion of Microscopic Particles in Disordered Systems | p. 423 |
| Dynamics of Microscopic Particles in Inhomogeneous Systems | p. 426 |
| Dynamic Properties of Microscopic Particles in a Random Inhomogeneous Media | p. 431 |
| Mean field method | p. 431 |
| Statistical adiabatic approximation | p. 433 |
| Inverse-scattering transformation based statistical perturbation theory | p. 436 |
| Microscopic Particles in Interacting Many-particle Systems | p. 438 |
| Effects of High-order Dispersion on Microscopic Particles | p. 444 |
| Interaction of Microscopic Particles and Its Radiation Effect in Perturbed Systems with Different Dispersions | p. 453 |
| Microscopic Particles in Three and Two Dimensional Nonlinear Media with Impurities | p. 459 |
| Bibliography | p. 467 |
| Nonlinear Quantum-Mechanical Properties of Excitons and Phonons | p. 471 |
| Excitons in Molecular Crystals | p. 471 |
| Raman Scattering from Nonlinear Motion of Excitons | p. 480 |
| Infrared Absorption of Exciton-Solitons in Molecular Crystals | p. 487 |
| Finite Temperature Excitonic Mossbauer Effect | p. 493 |
| Nonlinear Excitation of Excitons in Protein | p. 501 |
| Thermal Stability and Lifetime of Exciton-Soliton at Biological Temperature | p. 510 |
| Effects of Structural Disorder and Heart Bath on Exciton Localization | p. 520 |
| Effects of structural disorder | p. 521 |
| Influence of heat bath | p. 526 |
| Eigenenergy Spectra of Nonlinear Excitations of Excitons | p. 529 |
| Experimental Evidences of Exciton-Soliton State in Molecular Crystals and Protein Molecules | p. 536 |
| Experimental data in acetanilide | p. 536 |
| Infrared absorption and Raman spectra | p. 537 |
| Dynamic test of soliton excitation in acetanilide | p. 538 |
| Infrared and Raman spectra of collagen, E. coli. and human tissue | p. 541 |
| Infrared spectra of collagen proteins | p. 541 |
| Raman spectrum of collagen | p. 544 |
| Infrared radiation spectrum of human tissue and Raman spectrum of E. col. | p. 545 |
| Specific heat of ACN and protein | p. 547 |
| Properties of Nonlinear Excitations of Phonons | p. 549 |
| Bibliography | p. 551 |
| Properties of Nonlinear Excitations and Motions of Protons, Polarons and Magnons in Different Systems | p. 557 |
| Model of Excitation and Proton Transfer in Hydrogen-bonded Systems | p. 557 |
| Theory of Proton Transferring in Hydrogen Bonded Systems | p. 564 |
| Thermodynamic Properties and Conductivity of Proton Transfer | p. 572 |
| Properties of Proton Collective Excitation in Liquid Water | p. 577 |
| States and properties of molecules in liquid water | p. 578 |
| Properties of hydrogen-bonded closed chains in liquid water | p. 579 |
| Ring electric current and mechanism of magnetization of water | p. 581 |
| Nonlinear Excitation of Polarons and its Properties | p. 586 |
| Nonlinear Localization of Small Polarons | p. 593 |
| Nonlinear Excitation of Electrons in Coupled Electron-Electron and Electron-Phonon Systems | p. 596 |
| Nonlinear Excitation of Magnon in Ferromagnetic Systems | p. 601 |
| Collective Excitations of Magnons in Antiferromagnetic Systems | p. 607 |
| Bibliography | p. 613 |
| Table of Contents provided by Ingram. All Rights Reserved. |
