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.

1. A brief history of quantum tunneling -- 2. Some basic questions concerning quantum tunneling. 2.1. Tunneling and the uncertainty principle. 2.2. Asymptotic form of decay after a very long time. 2.3. Initial stages of decay. 2.4. Solvable models exhibiting different stages of decay -- 3. Simple solvable problems. 3.1. Confining double-well potentials. 3.2. Tunneling through barriers of finite extent. 3.3. Tunneling through a series of identical rectangular barriers. 3.4. Eckart's potential. 3.5. Double-well morse potential. 3.6. A solvable asymmetric double-well potential -- 4. Time-dependence of the wave function in one-dimensional tunneling. 4.1. Time-dependent tunneling for a [symbol]-function barrier. 4.2. An asymptotic expression in time for the transmission of a wave packet -- 5. Semiclassical approximations. 5.1. The WKB approximation. 5.2. Method of Miller and good. 5.3. Calculation of the splitting of levels in a symmetric double-well potential using WKB approximation. 5.4. Energy eigenvalues for motion in a series of identical barriers. 5.5. Tunneling in momentum space. 5.6. The Bremmer series -- 6. Generalization of the Bohr-Sommerfeld quantization rule and its applic…