Quantum Theory of Tunneling

In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined.

In addition, by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and nuclear physics are presented and solved.

Contents:

• A Brief History of Quantum Tunneling
• Some Basic Questions Concerning Quantum Tunneling
• Simple Solvable Problems
• Time-Dependence of the Wave Function in One-Dimensional Tunneling
• Semiclassical Approximations
• Generalization of the Bohr–Sommerfeld Quantization Rule and Its Application to Quantum Tunneling
• Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State
• Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable Barriers
• Classical Descriptions of Quantum Tunneling
• Tunneling in Time-Dependent Barriers
• Decay Width and the Scattering Theory
• The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems
• Path Integral and Its Semi-Classical Approximation in Quantum Tunneling
• Heisenberg's Equations of Motion for Tunneling
• Wigner Distribution Function in Quantum Tunneling
• Decay Widths of Siegert States, Complex Scaling and Dilatation Transformation
• Multidimensional Quantum Tunneling
• Group and Signal Velocities
• Time-Delay, Reflection Time Operator and Minimum Tunneling Time
• More About Tunneling Time
• Tunneling of a System with Internal Degrees of Freedom
• Motion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped Object
• Relativistic Formulation of Quantum Tunneling
• Inverse Problems of Quantum Tunneling
• Some Examples of Quantum Tunneling in Atomic and Molecular Physics
• Some Examples in Condensed Matter Physics
• Alpha Decay

Readership: Graduate students and researchers in theoretical, mathematical, condensed matter and nuclear physics, as well as theoretical chemistry.