Quantum theory of tunneling

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Quantum theory of tunneling / Mohsen Razavy

資料種別:: 図書
出版情報:: Singapore : World Scientific, c2003
形態:: xxi, 549 p. ; 25 cm
著者名:: Razavy, Mohsen
ISBN:: 9789812380197 [9812380191] (: pbk)
9789812380180 [9812380183] (: hard)
書誌ID:: BA61343070

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注記:

Includes bibliographies and index

主題:

Quantum theory; Tunneling (Physics)

言語:

英語

目次情報:

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：

Tunneling and the Uncertainty Principle / 2.1：

Decay of a Quasistationary State / 2.2：

Semi-Classical Approximations / 3：

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