What is included with this book?
Preface | p. v |
A Brief History of Quantum Tunneling | p. 1 |
Some Basic Questions Concerning Quantum Tunneling | p. 9 |
Tunneling and the Uncertainty Principle | p. 9 |
Decay of a Quasistationary State | p. 11 |
Semi-Classical Approximations | p. 23 |
The WKB Approximation | p. 23 |
Method of Miller and Good | p. 31 |
Calculation of the Splitting of Levels in a Symmetric Double-Well Potential Using WKB Approximation | p. 35 |
Generalization of the Bohr-Sommerfeld Quantization Rule and its Application to Quantum Tunneling | p. 41 |
The Bohr-Sommerfeld Method for Tunneling in Symmetric and Asymmetric Wells | p. 45 |
Numerical Examples | p. 48 |
Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State | p. 53 |
Solution of the Schrodinger Equation with Radiating Boundary Condition | p. 53 |
The Time Development of a Wave PacketTrapped Behind a Barrier | p. 57 |
A More Accurate Determination of the Wave Function of a Decaying State | p. 61 |
Some Instances Where WKB Approximation and the Gamow Formula Do Not Work | p. 66 |
Simple Solvable Problems | p. 73 |
Confining Double-Well Potentials | p. 73 |
Time-dependent Tunneling for a [delta]-Function Barrier | p. 79 |
Tunneling Through Barriers of Finite Extent | p. 82 |
Tunneling Through a Series of Identical Rectangular Barriers | p. 90 |
Eckart's Potential | p. 96 |
Double-Well Morse Potential | p. 99 |
Tunneling in Confining Symmetric and Asymmetric Double-Wells | p. 105 |
Tunneling When the Barrier is Nonlocal | p. 112 |
Tunneling in Separable Potentials | p. 116 |
A Solvable Asymmetric Double-Well Potential | p. 119 |
Quasi-Solvable Examples of Symmetric and Asymmetric Double-Wells | p. 121 |
Gel'fand-Levitan Method | p. 124 |
Darboux's Method | p. 127 |
Optical Potential Barrier Separating Two Symmetric or Asymmetric Wells | p. 128 |
A Classical Description of Tunneling | p. 139 |
Tunneling in Time-Dependent Barriers | p. 149 |
Multi-Channel Schrodinger Equation for Periodic Potentials | p. 150 |
Tunneling Through an Oscillating Potential Barrier | p. 152 |
Separable Tunneling Problems with Time-Dependent Barriers | p. 157 |
Penetration of a Particle Inside a Time-Dependent Potential Barrier | p. 162 |
Decay Width and the Scattering Theory | p. 167 |
Scattering Theory and the Time-Dependent Schrodinger Equation | p. 168 |
An Approximate Method of Calculating the Decay Widths | p. 173 |
Time-Dependent Perturbation Theory Applied to the Calculation of Decay Widths of Unstable States | p. 176 |
Early Stages of Decay via Tunneling | p. 181 |
An Alternative Way of Calculating the Decay Width Using the Second Order Perturbation Theory | p. 184 |
Tunneling Through Two Barriers | p. 186 |
Escape from a Potential Well by Tunneling Through both Sides | p. 191 |
Decay of the Initial State and the Jost Function | p. 196 |
The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems | p. 205 |
Mathematical Formulation | p. 206 |
Matrix Equations and Semi-classical Approximation for Many-Channel Problems | p. 212 |
Path Integral and Its Semi-Classical Approximation in Quantum Tunneling | p. 219 |
Application to the S-Wave Tunneling of a Particle Through a Central Barrier | p. 222 |
Method of Euclidean Path Integral | p. 226 |
An Example of Application of the Path Integral Method in Tunneling | p. 231 |
Complex Time, Path Integrals and Quantum Tunneling | p. 237 |
Path Integral and the Hamilton-Jacobi Coordinates | p. 241 |
Remarks About the Semi-Classical Propagator and Tunneling Problem | p. 243 |
Heisenberg's Equations of Motion for Tunneling | p. 251 |
The Heisenberg Equations of Motion for Tunneling in Symmetric and Asymmetric Double-Wells | p. 252 |
Tunneling in a Symmetric Double-Well | p. 258 |
Tunneling in an Asymmetric Double-Well | p. 259 |
Tunneling in a Potential Which Is the Sum of Inverse Powers of the Radial Distance | p. 261 |
Klein's Method for the Calculation of the Eigenvalues of a Confining Double-Well Potential | p. 267 |
Wigner Distribution Function in Quantum Tunneling | p. 277 |
Wigner Distribution Function and Quantum Tunneling | p. 281 |
Wigner Trajectory for Tunneling in Phase Space | p. 284 |
Wigner Distribution Function for an Asymmetric Double-Well | p. 290 |
Wigner Trajectory for an Oscillating Wave Packet | p. 290 |
Margenau-Hill Distribution Function for a Double-Well Potential | p. 292 |
Complex Scaling and Dilatation Transformation Applied to the Calculation of the Decay Width | p. 297 |
Multidimensional Quantum Tunneling | p. 307 |
The Semi-classical Approach of Kapur and Peierls | p. 307 |
Wave Function for the Lowest Energy State | p. 311 |
Calculation of the Low-Lying Wave Functions by Quadrature | p. 313 |
Method of Quasilinearization Applied to the Problem of Multidimensional Tunneling | p. 318 |
Solution of the General Two-Dimensional Problems | p. 323 |
The Most Probable Escape Path | p. 327 |
Group and Signal Velocities | p. 339 |
Time-Delay, Reflection Time Operator and Minimum Tunneling Time | p. 351 |
Time-Delay in Tunneling | p. 352 |
Time-Delay for Tunneling of a Wave Packet | p. 356 |
Landauer and Martin Criticism of the Definition of the Time-Delay in Quantum Tunneling | p. 365 |
Time-Delay in Multi-Channel Tunneling | p. 368 |
Reflection Time in Quantum Tunneling | p. 371 |
Minimum Tunneling Time | p. 375 |
More about Tunneling Time | p. 381 |
Dwell and Phase Tunneling Times | p. 382 |
Buttiker and Landauer Time | p. 385 |
Larmor Precession | p. 388 |
Tunneling Time and its Determination Using the Internal Energy of a Simple Molecule | p. 392 |
Intrinsic Time | p. 394 |
A Critical Study of the Tunneling Time Determination by a Quantum Clock | p. 398 |
Tunneling Time According to Low and Mende | p. 402 |
Tunneling of a System with Internal Degrees of Freedom | p. 411 |
Lifetime of Coupled-Channel Resonances | p. 411 |
Two-Coupled Channel Problem with Spherically Symmetric Barriers | p. 413 |
A Numerical Example | p. 415 |
Tunneling of a Simple Molecule | p. 418 |
Tunneling of a Molecule in Asymmetric Double-Wells | p. 424 |
Tunneling of a Molecule Through a Potential Barrier | p. 429 |
Antibound State of a Molecule | p. 434 |
Motion of a Particle in a Space Bounded by a Surface of Revolution | p. 439 |
Testing the Accuracy of the Present Method | p. 444 |
Calculation of the Eigenvalues | p. 445 |
Relativistic Formulation of Quantum Tunneling | p. 453 |
One-Dimensional Tunneling of the Electrons | p. 453 |
Tunneling of Spinless Particles in One Dimension | p. 458 |
Tunneling Time in Special Relativity | p. 461 |
The Inverse Problem of Quantum Tunneling | p. 471 |
A Method for Finding the Potential from the Reflection Amplitude | p. 472 |
Determination of the Shape of the Potential Barrier in One-Dimensional Tunneling | p. 473 |
Prony's Method of Determination of Complex Energy Eigenvalues | p. 476 |
A Numerical Example | p. 478 |
The Inverse Problem of Tunneling for Gamow States | p. 479 |
Some Examples of Quantum Tunneling in Atomic and Molecular Physics | p. 485 |
Torsional Vibration of a Molecule | p. 485 |
Electron Emission from the Surface of Cold Metals | p. 488 |
Ionization of Atoms in Very Strong Electric Field | p. 491 |
A Time-Dependent Formulation of Ionization in an Electric Field | p. 493 |
Ammonia Maser | p. 497 |
Optical Isomers | p. 500 |
Three-Dimensional Tunneling in the Presence of a Constant Field of Force | p. 501 |
Examples from Condensed Matter Physics | p. 511 |
The Band Theory of Solids and the Kronig-Penney Model | p. 511 |
Tunneling in Metal-Insulator-Metal Structures | p. 515 |
Many Electron Formulation of the Current | p. 516 |
Electron Tunneling Through Hetero-structures | p. 525 |
Alpha Decay | p. 531 |
Index | p. 541 |
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