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1.

図書

図書
Jan Cnops
出版情報: Boston : Birkhäuser, c2002  x, 211 p. ; 24 cm
シリーズ名: Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser ; v. 24
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Introduction
Clifford Algebras
Manifolds
Dirac Operators
Conformal Maps
Unique Continuation and the Cauchy Kernel
Boundary Values
Appendix
General Manifolds
The Additional Canterbury Tales
List of Symbols
Bibliography
Index
Introduction
Clifford Algebras
Manifolds
2.

図書

図書
Mohsen Razavy
出版情報: Singapore : World Scientific, c2003  xxi, 549 p. ; 25 cm
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Preface
A Brief History of Quantum Tunneling / 1:
Some Basic Questions Concerning Quantum Tunneling / 2:
Tunneling and the Uncertainty Principle / 2.1:
Decay of a Quasistationary State / 2.2:
Semi-Classical Approximations / 3:
The WKB Approximation / 3.1:
Method of Miller and Good / 3.2:
Calculation of the Splitting of Levels in a Symmetric Double-Well Potential Using WKB Approximation / 3.3:
Generalization of the Bohr-Sommerfeld Quantization Rule and its Application to Quantum Tunneling / 4:
The Bohr-Sommerfeld Method for Tunneling in Symmetric and Asymmetric Wells / 4.1:
Numerical Examples / 4.2:
Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State / 5:
Solution of the Schrodinger Equation with Radiating Boundary Condition / 5.1:
The Time Development of a Wave PacketTrapped Behind a Barrier / 5.2:
A More Accurate Determination of the Wave Function of a Decaying State / 5.3:
Some Instances Where WKB Approximation and the Gamow Formula Do Not Work / 5.4:
Simple Solvable Problems / 6:
Confining Double-Well Potentials / 6.1:
Time-dependent Tunneling for a [delta]-Function Barrier / 6.2:
Tunneling Through Barriers of Finite Extent / 6.3:
Tunneling Through a Series of Identical Rectangular Barriers / 6.4:
Eckart's Potential / 6.5:
Double-Well Morse Potential / 6.6:
Tunneling in Confining Symmetric and Asymmetric Double-Wells / 7:
Tunneling When the Barrier is Nonlocal / 7.1:
Tunneling in Separable Potentials / 7.2:
A Solvable Asymmetric Double-Well Potential / 7.3:
Quasi-Solvable Examples of Symmetric and Asymmetric Double-Wells / 7.4:
Gel'fand-Levitan Method / 7.5:
Darboux's Method / 7.6:
Optical Potential Barrier Separating Two Symmetric or Asymmetric Wells / 7.7:
A Classical Description of Tunneling / 8:
Tunneling in Time-Dependent Barriers / 9:
Multi-Channel Schrodinger Equation for Periodic Potentials / 9.1:
Tunneling Through an Oscillating Potential Barrier / 9.2:
Separable Tunneling Problems with Time-Dependent Barriers / 9.3:
Penetration of a Particle Inside a Time-Dependent Potential Barrier / 9.4:
Decay Width and the Scattering Theory / 10:
Scattering Theory and the Time-Dependent Schrodinger Equation / 10.1:
An Approximate Method of Calculating the Decay Widths / 10.2:
Time-Dependent Perturbation Theory Applied to the Calculation of Decay Widths of Unstable States / 10.3:
Early Stages of Decay via Tunneling / 10.4:
An Alternative Way of Calculating the Decay Width Using the Second Order Perturbation Theory / 10.5:
Tunneling Through Two Barriers / 10.6:
Escape from a Potential Well by Tunneling Through both Sides / 10.7:
Decay of the Initial State and the Jost Function / 10.8:
The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems / 11:
Mathematical Formulation / 11.1:
Matrix Equations and Semi-classical Approximation for Many-Channel Problems / 11.2:
Path Integral and Its Semi-Classical Approximation in Quantum Tunneling / 12:
Application to the S-Wave Tunneling of a Particle Through a Central Barrier / 12.1:
Method of Euclidean Path Integral / 12.2:
An Example of Application of the Path Integral Method in Tunneling / 12.3:
Complex Time, Path Integrals and Quantum Tunneling / 12.4:
Path Integral and the Hamilton-Jacobi Coordinates / 12.5:
Remarks About the Semi-Classical Propagator and Tunneling Problem / 12.6:
Heisenberg's Equations of Motion for Tunneling / 13:
The Heisenberg Equations of Motion for Tunneling in Symmetric and Asymmetric Double-Wells / 13.1:
Tunneling in a Symmetric Double-Well / 13.2:
Tunneling in an Asymmetric Double-Well / 13.3:
Tunneling in a Potential Which Is the Sum of Inverse Powers of the Radial Distance / 13.4:
Klein's Method for the Calculation of the Eigenvalues of a Confining Double-Well Potential / 13.5:
Wigner Distribution Function in Quantum Tunneling / 14:
Wigner Distribution Function and Quantum Tunneling / 14.1:
Wigner Trajectory for Tunneling in Phase Space / 14.2:
Wigner Distribution Function for an Asymmetric Double-Well / 14.3:
Wigner Trajectory for an Oscillating Wave Packet / 14.4:
Margenau-Hill Distribution Function for a Double-Well Potential / 14.5:
Complex Scaling and Dilatation Transformation Applied to the Calculation of the Decay Width / 15:
Multidimensional Quantum Tunneling / 16:
The Semi-classical Approach of Kapur and Peierls / 16.1:
Wave Function for the Lowest Energy State / 16.2:
Calculation of the Low-Lying Wave Functions by Quadrature / 16.3:
Method of Quasilinearization Applied to the Problem of Multidimensional Tunneling / 16.4:
Solution of the General Two-Dimensional Problems / 16.5:
The Most Probable Escape Path / 16.6:
Group and Signal Velocities / 17:
Time-Delay, Reflection Time Operator and Minimum Tunneling Time / 18:
Time-Delay in Tunneling / 18.1:
Time-Delay for Tunneling of a Wave Packet / 18.2:
Landauer and Martin Criticism of the Definition of the Time-Delay in Quantum Tunneling / 18.3:
Time-Delay in Multi-Channel Tunneling / 18.4:
Reflection Time in Quantum Tunneling / 18.5:
Minimum Tunneling Time / 18.6:
More about Tunneling Time / 19:
Dwell and Phase Tunneling Times / 19.1:
Buttiker and Landauer Time / 19.2:
Larmor Precession / 19.3:
Tunneling Time and its Determination Using the Internal Energy of a Simple Molecule / 19.4:
Intrinsic Time / 19.5:
A Critical Study of the Tunneling Time Determination by a Quantum Clock / 19.6:
Tunneling Time According to Low and Mende / 19.7:
Tunneling of a System with Internal Degrees of Freedom / 20:
Lifetime of Coupled-Channel Resonances / 20.1:
Two-Coupled Channel Problem with Spherically Symmetric Barriers / 20.2:
A Numerical Example / 20.3:
Tunneling of a Simple Molecule / 20.4:
Tunneling of a Molecule in Asymmetric Double-Wells / 20.5:
Tunneling of a Molecule Through a Potential Barrier / 20.6:
Antibound State of a Molecule / 20.7:
Motion of a Particle in a Space Bounded by a Surface of Revolution / 21:
Testing the Accuracy of the Present Method / 21.1:
Calculation of the Eigenvalues / 21.2:
Relativistic Formulation of Quantum Tunneling / 22:
One-Dimensional Tunneling of the Electrons / 22.1:
Tunneling of Spinless Particles in One Dimension / 22.2:
Tunneling Time in Special Relativity / 22.3:
The Inverse Problem of Quantum Tunneling / 23:
A Method for Finding the Potential from the Reflection Amplitude / 23.1:
Determination of the Shape of the Potential Barrier in One-Dimensional Tunneling / 23.2:
Prony's Method of Determination of Complex Energy Eigenvalues / 23.3:
The Inverse Problem of Tunneling for Gamow States / 23.4:
Some Examples of Quantum Tunneling in Atomic and Molecular Physics / 24:
Torsional Vibration of a Molecule / 24.1:
Electron Emission from the Surface of Cold Metals / 24.2:
Ionization of Atoms in Very Strong Electric Field / 24.3:
A Time-Dependent Formulation of Ionization in an Electric Field / 24.4:
Ammonia Maser / 24.5:
Optical Isomers / 24.6:
Three-Dimensional Tunneling in the Presence of a Constant Field of Force / 24.7:
Examples from Condensed Matter Physics / 25:
The Band Theory of Solids and the Kronig-Penney Model / 25.1:
Tunneling in Metal-Insulator-Metal Structures / 25.2:
Many Electron Formulation of the Current / 25.3:
Electron Tunneling Through Hetero-structures / 25.4:
Alpha Decay / 26:
Index
Preface
A Brief History of Quantum Tunneling / 1:
Some Basic Questions Concerning Quantum Tunneling / 2:
3.

図書

図書
Yakir Aharonov and Daniel Rohrlich
出版情報: Weinheim : Wiley-VCH, c2005  x, 289 p. ; 25 cm
シリーズ名: Physics textbook
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4.

図書

図書
Richard P. Feynman, Albert R. Hibbs ; emended by Daniel F. Styer
出版情報: Mineola, N.Y. : Dover Publications, 2010  xii, 371 p. ; 24 cm
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Preface
Preface to Emended Edition
The Fundamental Concepts of Quantum Mechanics / Chapter 1:
Probability in quantum mechanics / 1-1:
The uncertainty principle / 1-2:
Interfering alternatives / 1-3:
Summary of probability concepts / 1-4:
Some remaining thoughts / 1-5:
The purpose of this book / 1-6:
The Quantum-mechanical Law of Motion / Chapter 2:
The classical action / 2-1:
The quantum-mechanical amplitude / 2-2:
The classical limit / 2-3:
The sum over paths / 2-4:
Events occurring in succession / 2-5:
Some remarks / 2-6:
Developing the Concepts with Special Examples / Chapter 3:
The free particle / 3-1:
Diffraction through a slit / 3-2:
Results for a sharp-edged slit / 3-3:
The wave function / 3-4:
Gaussian integrals / 3-5:
Motion in a potential field / 3-6:
Systems with many variables / 3-7:
Separable systems / 3-8:
The path integral as a functional / 3-9:
Interaction of a particle and a harmonic oscillator / 3-10:
Evaluation of path integrals by Fourier series / 3-11:
The Schrödinger Description of Quantum Mechanics / Chapter 4:
The Schrödinger equation / 4-1:
The time-independent hamiltonian / 4-2:
Normalizing the free-particle wave functions / 4-3:
Measurements and Operators / Chapter 5:
The momentum representation / 5-1:
Measurement of quantum-mechanical variables / 5-2:
Operators / 5-3:
The Perturbation Method in Quantum Mechanics / Chapter 6:
The perturbation expansion / 6-1:
An integral equation for KV / 6-2:
An expansion for the wave function / 6-3:
The scattering of an electron by an atom / 6-4:
Time-dependent perturbations and transition amplitudes / 6-5:
Transition Elements / Chapter 7:
Definition of the transition element / 7-1:
Functional derivatives / 7-2:
Transition elements of some special functionals / 7-3:
General results for quadratic actions / 7-4:
Transition elements and the operator notation / 7-5:
The perturbation series for a vector potential / 7-6:
The hamiltonian / 7-7:
Harmonic Oscillators / Chapter 8:
The simple harmonic oscillator / 8-1:
The polyatomic molecule / 8-2:
Normal coordinates / 8-3:
The one-dimensional crystal / 8-4:
The approximation of continuity / 8-5:
Quantum mechanics of a line of atoms / 8-6:
The three-dimensional crystal / 8-7:
Quantum field theory / 8-8:
The forced harmonic oscillator / 8-9:
Quantum Electrodynamics / Chapter 9:
Classical electrodynamics / 9-1:
The quantum mechanics of the rediation field / 9-2:
The ground state / 9-3:
Interaction of field and matter / 9-4:
A single electron in a radiative field / 9-5:
The Lamb shift / 9-6:
The emission of light / 9-7:
Summary / 9-8:
Statistical Mechanics / Chapter 10:
The partition function / 10-1:
The path integral evaluation / 10-2:
Quantum-mechanical effects / 10-3:
Systems of several variables / 10-4:
Remarks on methods of derivation / 10-5:
The Variational Method / Chapter 11:
A minimum principle / 11-1:
An application of the variational method / 11-2:
The standard variational principle / 11-3:
Slow electrons in a polar crystal / 11-4:
Other Problems in Probability / Chapter 12:
Random pulses / 12-1:
Characteristic functions / 12-2:
Noise / 12-3:
Gaussian noise / 12-4:
Noise spectrum / 12-5:
Brownian motion / 12-6:
Quantum mechanics / 12-7:
Influence functionals / 12-8:
Influence functional from a harmonic oscillator / 12-9:
Conclusions / 12-10:
Appendix: Some Useful Definite Integrals
Appendix: Notes
Index
Preface
Preface to Emended Edition
The Fundamental Concepts of Quantum Mechanics / Chapter 1:
5.

図書

図書
B.S. Chandrasekhar
出版情報: Cambridge ; New York : Cambridge University Press, 1998  x, 254 p. ; 26 cm
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Preface
Introduction / 1:
Crystals / 2:
Particles and waves / 3:
The atom / 4:
Statistical physics / 5:
The quantum mechanical crystal / 6:
Copper wires and glass rods / 7:
Silver spoons and plastic spoons / 8:
Glass panes and aluminium foils / 9:
Electric bulbs and insulated cables / 10:
Magnets / 11:
Superconductors / 12:
Conclusion / 13:
Glossary
Preface
Introduction / 1:
Crystals / 2:
6.

図書

図書
Gary E. Bowman
出版情報: Oxford : Oxford University Press, 2008  xi, 208 p. ; 24 cm
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Preface
Introduction: Three Worlds / 1:
Worlds 1 and 2 / 1.1:
World 3 / 1.2:
Problems / 1.3:
The Quantum Postulates / 2:
Postulate 1: The Quantum State / 2.1:
Postulate 2: Observables, Operators, and Eigenstates / 2.2:
Postulate 3: Quantum Superpositions / 2.3:
Discrete Eigenvalues / 2.3.1:
Continuous Eigenvalues / 2.3.2:
Closing Comments / 2.4:
What Is a Quantum State? / 2.5:
Probabilities, Averages, and Uncertainties / 3.1:
Probabilities / 3.1.1:
Averages / 3.1.2:
Uncertainties / 3.1.3:
The Statistical Interpretation / 3.2:
Bohr, Einstein, and Hidden Variables / 3.3:
Background / 3.3.1:
Fundamental Issues / 3.3.2:
Einstein Revisited / 3.3.3:
The Structure of Quantum States / 3.4:
Mathematical Preliminaries / 4.1:
Vector Spaces / 4.1.1:
Function Spaces / 4.1.2:
Dirac's Bra-ket Notation / 4.2:
Bras and Kets / 4.2.1:
Labeling States / 4.2.2:
The Scalar Product / 4.3:
Quantum Scalar Products / 4.3.1:
Discussion / 4.3.2:
Representations / 4.4:
Basics / 4.4.1:
Superpositions and Representations / 4.4.2:
Representational Freedom / 4.4.3:
Operators / 4.5:
Introductory Comments / 5.1:
Hermitian Operators / 5.2:
Adjoint Operators / 5.2.1:
Hermitian Operators: Definition and Properties / 5.2.2:
Wavefunctions and Hermitian Operators / 5.2.3:
Projection and Identity Operators / 5.3:
Projection Operators / 5.3.1:
The Identity Operator / 5.3.2:
Unitary Operators / 5.4:
Matrix Mechanics / 5.5:
Elementary Matrix Operations / 6.1:
Vectors and Scalar Products / 6.1.1:
Matrices and Matrix Multiplication / 6.1.2:
Vector Transformations / 6.1.3:
States as Vectors / 6.2:
Operators as Matrices / 6.3:
An Operator in Its Eigenbasis / 6.3.1:
Matrix Elements and Alternative Bases / 6.3.2:
Change of Basis / 6.3.3:
Adjoint, Hermitian, and Unitary Operators / 6.3.4:
Eigenvalue Equations / 6.4:
Commutators and Uncertainty Relations / 6.5:
The Commutator / 7.1:
Definition and Characteristics / 7.1.1:
Commutators in Matrix Mechanics / 7.1.2:
The Uncertainty Relations / 7.2:
Uncertainty Products / 7.2.1:
General Form of the Uncertainty Relations / 7.2.2:
Interpretations / 7.2.3:
Reflections / 7.2.4:
Angular Momentum / 7.3:
Angular Momentum in Classical Mechanics / 8.1:
Basics of Quantum Angular Momentum / 8.2:
Operators and Commutation Relations / 8.2.1:
Eigenstates and Eigenvalues / 8.2.2:
Raising and Lowering Operators / 8.2.3:
Physical Interpretation / 8.3:
Measurements / 8.3.1:
Relating L[superscript 2] and L[subscript z] / 8.3.2:
Orbital and Spin Angular Momentum / 8.4:
Orbital Angular Momentum / 8.4.1:
Spin Angular Momentum / 8.4.2:
Review / 8.5:
The Time-Independent Schrodinger Equation / 8.6:
An Eigenvalue Equation for Energy / 9.1:
Using the Schrodinger Equation / 9.2:
Conditions on Wavefunctions / 9.2.1:
An Example: the Infinite Potential Well / 9.2.2:
Interpretation / 9.3:
Energy Eigenstates in Position Space / 9.3.1:
Overall and Relative Phases / 9.3.2:
Potential Barriers and Tunneling / 9.4:
The Step Potential / 9.4.1:
The Step Potential and Scattering / 9.4.2:
Tunneling / 9.4.3:
What's Wrong with This Picture? / 9.5:
Why Is the State Complex? / 9.6:
Complex Numbers / 10.1:
Polar Form / 10.1.1:
Argand Diagrams and the Role of the Phase / 10.1.3:
The Phase in Quantum Mechanics / 10.2:
Phases and the Description of States / 10.2.1:
Phase Changes and Probabilities / 10.2.2:
Unitary Operators Revisited / 10.2.3:
Unitary Operators, Phases, and Probabilities / 10.2.4:
Example: A Spin 1/2 System / 10.2.5:
Wavefunctions / 10.3:
Time Evolution / 10.4:
The Time-Dependent Schrodinger Equation / 11.1:
How Time Evolution Works / 11.2:
Time Evolving a Quantum State / 11.2.1:
Unitarity and Phases Revisited / 11.2.2:
Expectation Values / 11.3:
Time Derivatives / 11.3.1:
Constants of the Motion / 11.3.2:
Energy-Time Uncertainty Relations / 11.4:
Conceptual Basis / 11.4.1:
Spin 1/2: An Example / 11.4.2:
What is a Wavefunction? / 11.5:
Eigenstates and Coefficients / 12.1.1:
Representations and Operators / 12.1.2:
Changing Representations / 12.2:
Change of Basis Revisited / 12.2.1:
From x to p and Back Again / 12.2.2:
Gaussians and Beyond / 12.2.3:
Phases and Time Evolution / 12.3:
Free Particle Evolution / 12.3.1:
Wavepackets / 12.3.2:
Bra-ket Notation / 12.4:
Quantum States / 12.4.1:
Eigenstates and Transformations / 12.4.2:
Epilogue / 12.5:
Mathematical Concepts / 12.6:
Complex Numbers and Functions / A.1:
Differentiation / A.2:
Integration / A.3:
Differential Equations / A.4:
Quantum Measurement / B:
The Harmonic Oscillator / C:
Energy Eigenstates and Eigenvalues / C.1:
The Number Operator and its Cousins / C.2:
Photons as Oscillators / C.3:
Unitary Transformations / D:
Finite Transformations and Generators / D.1:
Continuous Symmetries / D.3:
Symmetry Transformations / D.3.1:
Symmetries of Physical Law / D.3.2:
System Symmetries / D.3.3:
Bibliography
Index
Preface
Introduction: Three Worlds / 1:
Worlds 1 and 2 / 1.1:
7.

図書

図書
Kalyan B. Sinha, Debashish Goswami
出版情報: Cambridge : Cambridge University Press, 2007  x, 290 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 169
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8.

図書

図書
Roger Penrose with Abner Shimony, Nancy Cartwright and Stephen Hawking ; edited by Malcolm Longair
出版情報: Cambridge : Cambridge University Press, 2000  xxii, 201 p. ; 22 cm
シリーズ名: Canto
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9.

図書

図書
edited by Jørgen Kalckar
出版情報: Amsterdam : Elsevier, 2008  2 v. ; 27 cm
シリーズ名: Collected works / Niels Bohr ; general editor, L. Rosenfeld ; v. 6-7
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10.

図書

図書
Franz Schwabl ; translated by Roginald Hilton and Angela Lahee
出版情報: Berlin ; New York : Springer, c1999  xv, 405 p. ; 25 cm
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目次情報:
Nonrelativistic multi-particle-systems
Relativistic wave equations
Relativistic fields
Nonrelativistic multi-particle-systems
Relativistic wave equations
Relativistic fields
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