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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:
2.

図書

図書
Barry Simon
出版情報: Providence, R.I. : AMS Chelsea Pub., American Mathematical Society, c2005  xi, 306 p. ; 26 cm
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目次情報: 続きを見る
Preface to Second Edition
Preface
List of Symbols
Introduction / I:
Construction of Gaussian Processes / 1:
Some Fundamental Tools of Probability Theory / 3:
The Basic Processes / II:
The Wiener Process, the Oscillator Process, and the Brownian Bridge / 4:
Regularity Properties-1 / 5:
The Feynman-Kac Formula / 6:
Regularity and Recurrence Properties-2 / 7:
Bound State Problems / III:
The Birman-Schwinger Kernel and Lieb's Formula / 8:
Phase Space Bounds / 9:
The Classical Limit / 10:
Recurrence and Weak Coupling / 11:
Inequalities / IV:
Correlation Inequalities / 12:
Other Inequalities: Log Concavity, Symmetric Rearrangement, Conditioning, Hypercontractivity / 13:
Magnetic Fields and Stochastic Integrals / V:
Ito's Integral / 14:
Schrodinger Operators with Magnetic Fields / 15:
Introduction to Stochastic Calculus / 16:
Asymptotics / VI:
Donsker's Theorem / 17:
Laplace's Method in Function Space / 18:
Introduction to the Donsker-Varadhan Theory / 19:
Other Topics / VII:
Perturbation Theory for the Ground State Energy / 20:
Dirichlet Boundaries and Decoupling Singularities in Scattering Theory / 21:
Crushed Ice and the Wiener Sausage / 22:
The Statistical Mechanics of Charged Particles with Positive Definite Interactions / 23:
An Introduction to Euclidean Quantum Field Theory / 24:
Properties of Eigenfunctions, Wave Packets, and Green's Functions / 25:
Inverse Problems and the Feynman-Kac Formula / 26:
References
Index
Bibliographic Supplement
Bibliography
Preface to Second Edition
Preface
List of Symbols
3.

図書

図書
Alastair I.M. Rae
出版情報: Cambridge : Cambridge University Press, 2004  xiii, 155 p. ; 22 cm
シリーズ名: Canto
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4.

図書

図書
George F. Koster ... [et al.]
出版情報: Cambridge, Mass. : M.I.T. Press, 1963  104 p. ; 24 cm
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5.

図書

図書
S.N. Khanna, A.W. Castleman, Jr. [(eds.)]
出版情報: Berlin : Springer, c2003  xii, 265 p. ; 24 cm
シリーズ名: Springer series in cluster physics
Physics and astronomy online library
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6.

図書

図書
John C. Slater
出版情報: New York ; Tokyo : McGraw-Hill, c1974  xvii, 583 p. ; 24 cm
シリーズ名: International series in pure and applied physics ; . Quantum theory of molecules and solids ; v. 4
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7.

図書

図書
edited by George T. Rado, Harry Suhl
出版情報: New York : Academic Press, 1963  xv, 623 p. ; 24 cm
シリーズ名: Magnetism / edited by George T. Rado, Harry Suhl ; v. 3
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8.

図書

図書
by F.J. Belinfante
出版情報: Oxford : Pergamon Press, 1973  xix, 354 p. ; 25 cm
シリーズ名: International series of monographs in natural philosophy ; v. 55
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9.

図書

図書
Frank J. Bockhoff
出版情報: Reading, Mass. : Addison-Wesley, [1969]  ix, 304 p. ; 24 cm
シリーズ名: Addison-Wesley series in chemistry
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10.

図書

図書
Joseph Callaway
出版情報: New York : Academic Press, 1974  2 v. ; 24 cm
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