Preface -- Contents -- Introduction -- Chapter 1 A Brief History of Quantum Tunneling -- Bibliography -- Chapter 2 Some Basic Questions Concerning Quantum Tunneling -- 2.1 Tunneling and the Uncertainty Principle -- 2.2 Decay of a Quasistationary State -- Bibliography -- Chapter 3 Semi-Classical Approximations -- 3.1 The WKB Approximation -- 3.2 Method of Miller and Good -- 3.3 Calculation of the Splitting of Levels in a Symmetric Double-Well Potential Using WKB Approximation -- Bibliography -- Chapter 4 Generalization of the Bohr-Sommerfeld Quantization Rule and its Application to Quantum Tunneling -- 4.1 The Bohr-Sommerfeld Method for Tunneling in Symmetric and Asymmetric Wells -- 4.2 Numerical Examples -- Bibliography -- Chapter 5 Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State -- 5.1 Solution of the Schrödinger Equation with Radiating Boundary Condition -- 5.2 The Time Development of a Wave Packet Trapped Behind a Barrier -- 5.3 A More Accurate Determination of the Wave Function of a Decaying State -- 5.4 Some Instances Where WKB Approximation and the Gamow Formula Do Not Work -- Bibliography -- Chapter 6 Simple Solvable Problems -- 6.1 Confining Double-Well Potentials -- 6.2 Time-dependent Tunneling for a -Function Barrier -- 6.3 Tunneling Through Barriers of Finite Extent -- 6.4 Tunneling Through a Series of Identical Rectangular Barriers -- 6.5 Eckart's Potential -- 6.6 Double-Well Morse Potential -- Bibliography -- Chapter 7 Tunneling in Confining Symmetric and Asymmetric Double-Wells -- 7.1 Tunneling When the Barrier is Nonlocal -- 7.2 Tunneling in Separable Potentials -- 7.3 A Solvable Asymmetric Double-Well Potential -- 7.4 Quasi-Solvable Examples of Symmetric and Asymmetric Double-Wells -- 7.5 Gel'fand-Levitan Method -- 7.6 Darboux's Method.

7.7 Optical Potential Barrier Separating Two Symmetric or Asymmetric Wells -- Bibliography -- Chapter 8 A Classical Description of Tunneling -- Bibliography -- Chapter 9 Tunneling in Time-Dependent Barriers -- 9.1 Multi-Channel Schrödinger Equation for Periodic Potentials -- 9.2 Tunneling Through an Oscillating Potential Barrier -- 9.3 Separable Tunneling Problems with Time-Dependent Barriers -- 9.4 Penetration of a Particle Inside a Time-Dependent Potential Barrier -- Bibliography -- Chapter 10 Decay Width and the Scattering Theory -- 10.1 Scattering Theory and the Time-Dependent Schrödinger Equation -- 10.2 An Approximate Method of Calculating the Decay Widths -- 10.3 Time-Dependent Perturbation Theory Applied to the Calculation of Decay Widths of Unstable States -- 10.4 Early Stages of Decay via Tunneling -- 10.5 An Alternative Way of Calculating the Decay Width Using the Second Order Perturbation Theory -- 10.6 Tunneling Through Two Barriers -- 10.7 Escape from a Potential Well by Tunneling Through both Sides -- 10.8 Decay of the Initial State and the Jost Function -- Bibliography -- Chapter 11 The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems -- 11.1 Mathematical Formulation -- 11.2 Matrix Equations and Semi-classical Approximation for Many-Channel Problems -- Bibliography -- Chapter 12 Path Integral and Its Semi-Classical Approximation in Quantum Tunneling -- 12.1 Application to the S-Wave Tunneling of a Particle Through a Central Barrier -- 12.2 Method of Euclidean Path Integral -- 12.3 An Example of Application of the Path Integral Method in Tunneling -- 12.4 Complex Time, Path Integrals and Quantum Tunneling -- 12.5 Path Integral and the Hamilton-Jacobi Coordinates -- 12.6 Remarks About the Semi-Classical Propagator and Tunneling Problem -- Bibliography.

Chapter 13 Heisenberg's Equations of Motion for Tunneling -- 13.1 The Heisenberg Equations of Motion for Tunneling in Symmetric and Asymmetric Double-Wells -- 13.2 Tunneling in a Symmetric Double-Well -- 13.3 Tunneling in an Asymmetric Double-Well -- 13.4 Tunneling in a Potential Which Is the Sum of Inverse Powers of the Radial Distance -- 13.5 Klein's Method for the Calculation of the Eigenvalues of a Confining Double-Well Potential -- Bibliography -- Chapter 14 Wigner Distribution Function in Quantum Tunneling -- 14.1 Wigner Distribution Function and Quantum Tunneling -- 14.2 Wigner Trajectory for Tunneling in Phase Space -- 14.3 Wigner Distribution Function for an Asymmetric Double-Well -- 14.4 Wigner Trajectory for an Oscillating Wave Packet -- 14.5 Margenau-Hill Distribution Function for a Double-Well Potential -- Bibliography -- Chapter 15 Complex Scaling and Dilatation Transformation Applied to the Calculation of the Decay Width -- Bibliography -- Chapter 16 Multidimensional Quantum Tunneling -- 16.1 The Semi-classical Approach of Kapur and Peierls -- 16.2 Wave Function for the Lowest Energy State -- 16.3 Calculation of the Low-Lying Wave Functions by Quadrature -- 16.4 Method of Quasilinearization Applied to the Problem of Multidimensional Tunneling -- 16.5 Solution of the General Two-Dimensional Problems -- 16.6 The Most Probable Escape Path -- Bibliography -- Chapter 17 Group and Signal Velocities -- Bibliography -- Chapter 18 Time-Delay, Reflection Time Operator and Minimum Tunneling Time -- 18.1 Time-Delay in Tunneling -- 18.2 Time-Delay for Tunneling of a Wave Packet -- 18.3 Landauer and Martin Criticism of the Definition of the Time-Delay in Quantum Tunneling -- 18.4 Time-Delay in Multi-Channel Tunneling -- 18.5 Reflection Time in Quantum Tunneling -- 18.6 Minimum Tunneling Time -- Bibliography -- Chapter 19 More about Tunneling Time.

19.1 Dwell and Phase Tunneling Times -- 19.2 Büttiker and Landauer Time -- 19.3 Larmor Precession -- 19.4 Tunneling Time and its Determination Using the Internal Energy of a Simple Molecule -- 19.5 Intrinsic Time -- 19.6 A Critical Study of the Tunneling Time Determination by a Quantum Clock -- 19.7 Tunneling Time According to Low and Mende -- Bibliography -- Chapter 20 Tunneling of a System with Internal Degrees of Freedom -- 20.1 Lifetime of Coupled-Channel Resonances -- 20.2 Two-Coupled Channel Problem with Spherically Symmetric Barriers -- 20.3 A Numerical Example -- 20.4 Tunneling of a Simple Molecule -- 20.5 Tunneling of a Molecule in Asymmetric Double-Wells -- 20.6 Tunneling of a Molecule Through a Potential Barrier -- 20.7 Antibound State of a Molecule -- Bibliography -- Chapter 21 Motion of a Particle in a Space Bounded by a Surface of Revolution -- 21.1 Testing the Accuracy of the Present Method -- 21.2 Calculation of the Eigenvalues -- Bibliography -- Chapter 22 Relativistic Formulation of Quantum Tunneling -- 22.1 One-Dimensional Tunneling of the Electrons -- 22.2 Tunneling of Spinless Particles in One Dimension -- 22.3 Tunneling Time in Special Relativity -- Bibliography -- Chapter 23 The Inverse Problem of Quantum Tunneling -- 23.1 A Method for Finding the Potential from the Reflection Amplitude -- 23.2 Determination of the Shape of the Potential Barrier in One-Dimensional Tunneling -- 23.3 Prony's Method of Determination of Complex Energy Eigenvalues -- 23.4 A Numerical Example -- 23.5 The Inverse Problem of Tunneling for Gamow States -- Bibliography -- Chapter 24 Some Examples of Quantum Tunneling in Atomic and Molecular Physics -- 24.1 Torsional Vibration of a Molecule -- 24.2 Electron Emission from the Surface of Cold Metals -- 24.3 Ionization of Atoms in Very Strong Electric Field.

24.4 A Time-Dependent Formulation of Ionization in an Electric Field -- 24.5 Ammonia Maser -- 24.6 Optical Isomers -- 24.7 Three-Dimensional Tunneling in the Presence of a Constant Field of Force -- Bibliography -- Chapter 25 Examples from Condensed Matter Physics -- 25.1 The Band Theory of Solids and the Kronig-Penney Model -- 25.2 Tunneling in Metal-Insulator-Metal Structures -- 25.3 Many Electron Formulation of the Current -- 25.4 Electron Tunneling Through Heterostructures -- Bibliography -- Chapter 26 Alpha Decay -- Bibliography -- Index.