Advances in Quantum Mechanics

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Section 1 The Classical-Quantum Correspondence Chapter 1Classical and Quantum Conjugate Dynamics – The Interplay Between Conjugate Variables 1. Introduction 1.1. Conjugate variables 1.2. Conjugate coordinate systems 1.3. The interplay between conjugate variables 1.4. Conjugate motions 1.5. Poisson brackets and commutators 1.6. The commutator as a derivation and its consequences 2. Quantum systems 3. Time evolution using energy and time eigenstates 4. Concluding remarks Author details References Chapter 2Classical and Quantum Correspondence in Anisotropic Kepler Problem Chapter 3Charathéodory’s “Royal Road” to the Calculus of Variations: A Possible Bridge Between Classical and Quantum Physics Chapter 4The Improvement of the Heisenberg Uncertainty Principle Section 2 The Schrödinger Equation Chapter 5Schrödinger Equation as a Hamiltonian System, Essential Nonlinearity, Dynamical Scalar Product and some Ideas of Decoherence Chapter 6Schrödinger Equation and (Future) Quantum Physics Chapter 7Quantum Damped Harmonic Oscillator Section 3 Path Integrals Chapter 8The Schwinger Action Principle and Its Applications to Quantum Mechanics Chapter 9Generalized Path Integral Technique: Nanoparticles Incident on a Slit Grating, Matter Wave Interference 1. Introduction 2. Generalized path integral 2.1. Expansion of the path integral 2.1.1. Temperature is zero 2.1.2. Temperature is not zero 2.2. Paths through N-slit grating 2.2.1. Passing of a particle through slit 2.2.2. Definition of new working parameters 3. Wave function behind the grating 4. Bohmian trajectories and variance of momenta and positions along paths 4.1. Dispersion of trajectories and the uncertainty principle 5. Concluding remarks Acknowledgement Author details References Chapter 10Quantum Intentionality and Determination of Realities in the Space-Time Through Path Integrals and Their Integral Transforms Section 4 Perturbation Theory Chapter 11Convergence of the Neumann Series for the Schrödinger Equation and General Volterra Equations in Banach Spaces Chapter 12Quantum Perturbation Theory in Fluid Mixtures 1. Introduction 2. Quantum correction term 2.1. Wigner-Kirkwood expansion 2.2. Free energy 3. Framework 3.1. Potentials 4. Results 5. Conclusion 6. Applications Author details References Chapter 13Quantal Cumulant Mechanics as Extended Ehrenfest Theorem 1. Introduction 2. Theoretical background 2.1. Heisenberg’ equation of motion and Ehrenfest theorem 2.2. Quantized Hamilton dynamics and quantal cumulant dynamics 2.3. Energy conservation law and least uncertainty state 2.4. Distribution function and joint distribution 2.5. Extension to multi-dimensional systems 3. Applications 3.1. Application to molecular vibration 3.2. Proton transfer reaction in guanine-cytosine base pair 3.3. Quantal structural transition of finite clusters 4. Summary Author details References Chapter 14Unruh Radiation via WKB Method Section 5 Foundations of Quantum Mechanics Chapter 15A Basis for Statistical Theory and Quantum Theory Chapter 16Relational Quantum Mechanics Chapter 17On the Dual Concepts of 'Quantum State' and 'Quantum Process' 1. Introduction 2. More about photons 3. On the arrow of time 4. More about the hydrogen atom 5. Quantum chemistry 6. Conclusion Author details References Chapter 18The Computational Unified Field Theory (CUFT): A Candidate 'Theory of Everything' 1. Introduction 2. The universal computational principle's D2 A–causal computation 3. The exhaustiveness of the universal consciousness principle for all natural phenomena 4. The universal computational principle's paradigmatic shift: Transcending cartesian dualism 5. The CUFT's sixth postulate: 'Ontological relativism' 6. The seventh postulate: “Universal Consciousness Spectrum (UCS)” 7. Critical Predictions of the 'Universal Consciousness Spectrum' 8. The scientific implications of the CUFT's universal consciousness principle 8.1. A singular 'A–causal' universal consciousness principle computation of all inductive and deductive 'X–Y' relationships 8.2. The "universal consciousness principle's computational program" 9. Theoretical ramifications of the universal consciousness principle 10. The CUFT's eighth postulate: The 'universal consciousness reality' Author details References Chapter 19Emergent un-Quantum Mechanics Chapter 20The Wigner-Heisenberg Algebra in Quantum Mechanics Chapter 21New System-Specific Coherent States by Supersymmetric Quantum Mechanics for Bound State Calculations Section 6 Quantization and Entanglement Chapter 22Quantum Dating Market Chapter 23Quantization as Selection Rather than Eigenvalue Problem 1. Introduction 2. Elements of an Eulerian representation of classical mechanics 2.1. Euler’s axioms 2.2. Eulerian principles of change of state for single bodies 2.3. Eulerian principles of change of state for Hamiltonian systems 3. Quantization as selection problem — I. Derivation of the stationary Schrödinger equation 3.1. The relationship between CM and non-CM as selection problem 3.1.1. Selection problem between Newtonian and non-Newtionian CM 3.1.2. Einsteinian selection problem between CM and non-CM 3.1.3. Selection problem between CM and non-CM in terms of allowed configurations 3.1.4. Selection problem between mechanics and non-mechanics 3.2. Non-classical representation of the potential and kinetic energies 3.3. The stationary Schrödinger equation 4. Quantization as selection problem — II. Non-classical solution to the stationary Schrödinger equation 4.1. The linear oscillator 4.2. The mathematically distinguished solutions 4.3. The physically distinguished solutions 4.4. The non-classical potential energy and the tunnel effect 5. The time dependent case 5.1. The time dependence of the stationary states 5.2. The equation-of-state-change 5.3. Derivation of the time-dependent Schrödinger equation 6. Summary and conclusions Author details References Chapter 24Entanglement, Nonlocality, Superluminal Signaling and Cloning Chapter 25The Husimi Distribution: Development and Applications Section 7 Quantum Information and Related Topics Chapter 26The Quantum Mechanics Aspect of Structural Transformations in Nanosystems 1. Introduction 2. Quasiclosed ensembles 3. Adiabatic approximation 4. Estimation of the number G(0) of different quasiclosed ensembles 5. Model spectrum for the description of configurational excitations 6. On the temperature ranges of melting and softening 7. Admissible states 8. Conclusions Author details References Chapter 27Decoding the Building Blocks of Life from the Perspective of Quantum Information 1. Introduction 2. Information-theoretical measures and complexities 3. Aminoacids 3.1. Physical and information-theoretical properties 3.2. Homochirality 4. Genetic code 4.1. Codons 4.2. Physical and information-theoretical properties 5. Concluding remarks Author details References Chapter 28The Theoretical Ramifications of the Computational Unified Field Theory 1. Introduction 2. A singular 'a-causal' universal consciousness principle computation of all inductive and deductive 'x-y' relationships 3. The "universal consciousness principle's computational program" 4. Theoretical ramifications of the universal consciousness principle Author details References Chapter 29Shannon Informational Entropies and Chemical Reactivity Chapter 30A Novel Isospectral Deformation Chain in Supersymmetric Quantum Mechanics Chapter 31Quantum Effects Through a Fractal Theory of Motion 1. Introduction 2. Covariant total derivative 3. Fractal space-time and the motion equation of free particles in the dissipative approximation 3.1. Solving the Schrödinger type equation by means of the WKBJ approximation method 3.2. Velocity potential γ (x) and the bound states 3.3. Velocity potential γ (x) and the quantum barrier 4. Casimir type effect in scale relativity theory 5. Fractal approximation of motion in mass transfer: release of drug from polimeric matrices 5.1. The dissipative approximation 5.1.1.Standard “diffusion” type equation. Fick type law 5.1.2. Anomalous “diffusion” type equation. Weibull relation 5.1.3. The correspondence between theoretical model and experimental results 5.2. The dispersive approximation 5.2.1. The correspondence between theoretical model and experimental results 6. Conclusions Author details References